Title THERMODYNAMIC PROPERTIES AND

Title
Author(s)
THERMODYNAMIC PROPERTIES AND PHASE
TRANSITIONS OF SOLID HYDROGEN HALIDES AND
THEIR DEUTERIUM ANALOGS
Inaba, Akira
Citation
Issue Date
Text Version ETD
URL
http://hdl.handle.net/11094/27733
DOI
Rights
Osaka University
丁HERMODYNAMIC
PROPERTIIES AND PHASE TRANSItt10NS
OF SOLID HYDROGttN HALIDES AND ttHEIR DEUTERIUM ANALOCS
A Thesis
Submitted. to
Osaka University
in Partial Fulfilment of the Requirements
for the, Degree
of
Doctor of Science
by
AKIRA INABA
[■
976]
Doctoral Committee:
Professor Hideaki Chihara, Chairman
Professor Sy0z6 seki
Professor RY6iti KiriYama
Associate Professor Nobuo
,7'/sc01931
Nakamura
ACKNOWLEDGMENTS
in this thesis have been carried
out und.er the direction of Professor Hideaki Chihara.
hi" sincere gratitude
The author would 1i-ke'to
"*pr""s
to Professor Chihara for his pat,ient guidance and
kind encouragement. Thanks are also due to Associate
The works d.escribed
Professor Nobuo Nakamura for his valuable suggestions
and discussions. The author would like to express
his gratit,ud.e to Dr. Tooru Atake for assistance in
experiments. The author also wishes to thank
P.rofessor Sy0z6 Seki and Associate Professor Hiroshi
Suga and the members of both the Professor Chihara's
and Seki's laboratories forb,heir encouragement and
fruitful discussions, Fina1ly, the author expresses
thanks to his wife Kiyoko anrl their daughter Kazuko
for their encouragement
，ユ
CONTENTS
CHAPTER
R
CHAPTER
..........
2. Experimental .....
2-L. Materials ......'.........o.......o..r......c
"
o....... !..
2-2. Calorimgter .. .....................
o.
2-3. Temperature scales .............
2-4. Heat capacity measurements ...................
2-5. Vapor pressurg measuremgnts .. o.... o..........
o... o. o... '..... o.
2-6. Dilatometry ................
o........ '.... o..
Refergnces to chapter 2 ...........
49
50
54
57
58
60
２
６
３
７
[iil
45
3. Thermodynamic Properties of HCI and DC1
............
.....
3-1. Heat capacj.ty
.. o.............
3-2. Vapor pressure ..........
44
■
６
CHAPTER
1
...,..............
1. IntrOduCtOry RemarkS .....
2
:....
1-1. Introduction .....
.....,.. 4
l-2. Review of previous works r.......r.
.. - -. -. -. o 4
l-2-L. Diffraction studies ..........
L-2-2. Infrared and Raman spectral studies '. .... ?. 2.3
..... . 27
I-2-3. Resonance studies ..........
..... 32
L-2-4. Dielectric measurements ... '.
1-2-5.Theoretica1worksonphasetransitions
38
1-3. Purpose of the present investigation .........
40
References to chapter I .... o.....
3-3. Enthalpy of fusion and transition
3-4. 120 K transition in HCl ,. o..
3-5. Thermod,ynamic functions' ...........
References to chapter 3 .....:....
Appendix 3A. t4easured. heat capacities
Appendix 38. Measured heat capacities
CHAPTER
CHAPTER
79
.....
..... 91
o
...... r...... 94
of HCl
' 95
of DCI .. r '. L02
4. Thermodynamic Properties of HBr and DBr ......c
.
.....
..........
4-L. Heat capacity
4-2. Vapor pressure .o........................
.
4-3. Enthalpy of fusion . . o o...... o.. o......
.............
4-4. Transitions in solids
.
4-5. Thermod.ynamic functions .o.........o...
.......
References to chapter 4 .. ....... o.....
Appendix 4A. Measured. heat capacities of HBr
Appendix 48. Measured heat capacities of DBr .....
L08
109
L20
L26
131
140
145
L46
L57
168
5. Thermodynamic Properties of III and DI
169
o..... o............
5-1. Heat capacity .............
..... . L79
o.
5-2. Vapor pressure .................
. 183
5-3. Enthalpy of fusion o......'.............
a e 188
5-4. Transition in solids .. o..... o.. o..........
...... L96
5-5. Thermod.ynamic functions..o..
20L
.......
..........
References to chapter 5
Appendix 5A. Measured heat capacities of HI ..... . 242
Append.ix 58. Measured heat capacities of DI ..... . 2L2
[i■ il
CHAPTER
6.
Properties and
Phase Transitions
--.; fina[ysis and Discussion
Thermodynamic
. . . . . . . . r . . 2L9
220
6-1. Ggneral remarks ........... ....- o. ............
....... 22L
6-2. Low temperature region :....
. 22L
.....
6-2-L. Zero point properties
. 229
6-2-2. The estimation of (Cp-Cv) correction
6-2-3. Librational contribution to
234
o................
heat capacity
6-2-4. The temperature dependence of 0o(T) ....... 237
. 246
6-2-5. Onset of orientational disord.er
o.... . 252
6-3. High ternperature region .....
r 255
6-4. fransition temperature region ..............
6-4-1. Extraction of anomal-ous part of
Cp a,￨,,tFan,ili° n… ……………………00250
工工エーII
Phase transition
6-4-2.
The
6-4・ 3.
The thermodynamic properties of
。..。 ●。o
o o o●
00●
....
the transitions ..... o....
roooe
6-4-4. Local ord.er in phase I .....
6-5. Mechanism of the phase transitions ....o
5-5-1. The d,isordering process ................a..
6-5-2. Phase transitions and molecular
[iv]
0 262
d
265
273
278
278
ABSTRACT
In the introductory chapter, a review j.s given on
the earlier works for solid hydrogen halides;
with a special emphasis on their structures,
molecular motions, molecular interactions, and
phase transitions.
of heat capacity
and vapor pressure of, hydrogen halides. A calibration
of the platinum and the germanium resistance
thermometers used will also be d.escribed.
In chapters 3 to 5, the thermodynamic properties
Chapter 2
is devoted to
measurements
obtained are presented. Discussions are given on
the "120 K transition" of single crystal IICI and
features of the other phase transitions.
In the last chapter, analyses of thermodynamic
properties are made primarily in order to elucidate
the mechanism of phase transitions. Both the heat
capacity and, the entropy of transitions extracted
suggested. the orientational ord,er-disorder type of
mechanism. Our discussions will extend to understanding
of the successive phase transitions in terms of
molecular interactions.
[V]
CHAPTER
■
Introductory Remarks
[■
]
1-1. Introduction
■
A hydrogen halide or deuterium. halide molecule
will be treated as a quasi-sphere, though it is
a diatomic mo1ecule, with a protuberance corresponding
to the position of the proton or deuteron. In fact,
all the solids in phase I are plastic according to
definition by Timmermurrjl) on the other hand, the
molecular d.ipole and the quadrupole moment are
significant in molecules HCl, HBr, ana urJ2)
The former decreases in this ord,er and the latter
in a reverse order. When being deuterated, the moment
of inerLia of each molecule is approximately doubled.
In solid., moreover, the existence of hydrogen bonds
plays an important role in its properties. Therefore,
systematic stud.ies of a series of hyd.rogen halides
and deuterium halides will make clear the interactions
in solid, the molecular motion, and the mechanism of
transitions.
Phase transitions in solid. hydrogen halides and
deuterium halides were discovered by calorimetric
stud.ies in 1920's and 1947, respectively. Their
transition and triple point temperatures are shown
in t,able 1-1. Each temperature values are given from
present results as will be described below.
A mile-stone in the hisLory of investigations may
[2]
TABLE
I-1.
Transi,tion and triple point temperatures
in hydrogen halides.
(in the unit of
K)
98.67
工
■59305
■iq.
DC■ 工エエ ■04.63
エ
■58。 4■
■土q.
エ
■86。
50
■iq.
HC■ 工工工
工1 ■■7e00
HBr III
89。
53
工工
■■3.60
DBr IIエ
93。
67
工工
■■9。
96
工
■85。
64
■■q.
HI
70.23
工I
■25。
60
工
222。
50
■■q.
77.48
工工
■28。
24
エ
221。 5■
1土 q.
D工
III
工工工
be set in the year of L967. At this turning point,
neutron d.iffraction stud.ies were for the first time
conducted by SAndor and
his coworkers
when the
positions of d.euterons were determined. In
L969,
subsequently, ferroelectricity of HCI and HBr in phase
his coworkers.
These investigations promoted the studies on the phase
transition mechanism from a microscopic point of view.
A review will be given below on the previous
III
was d.iscovered. by Hoshino and
investigations.
[3]
■-2:
Review of prё vious works
■-2-■
X―
,
DiffractiOn studies
ray studies before 1967
The ear■ iest diffraction studies were carried out
b, simon et a■ . atta Natta∫
3-9)・
The x_rよ y deteiminatiO.,
of the struCture Of hydrogen ha■ ide crysta■ s werel not
ёntirely
satisfaCtOry′ the different observers did n6t
agree among themse■ ves and moreover some resu■ ts werё
not in accord "ith the correspOnding tteasurements using
) Thus′ Natta fOund a cubic
the po■ ar■ zlAし m■ cloも cOle`子
工工 Whereas
structure for HBr in phase
Optica■ ■y anisotropic.
(ii)fOr HBr and Hェ
To sum up thё resu■ ts obtainedF
ёubic
(1)phage tt has the
the materia■ is
face centered structureF
′ phaSe 工■ has probab■ y
the tetragOna■
face centered structure with c/a 1 l but the deformation
re■ ative
to phase tt iS not ■arge, (i■ i)phaSe ェェエ has
a 60mp■ ioited structtre which′ probab■ y apprOx■mateS
to tetragonal face Centered
ratio c/a >
■attide
with the axia■
■。
x=ray attd neutron studies by Sandor and his coworkeFs
The
c■
こtructura■ ana■ yses by X― ray
ue to the
re■ iab■ e
■ocation
diffraCtion gave no
Of the hydrOgen atoⅢ S・
平9re
ana■ yses shou■ d be made by ,ettrOn diffr● Ctio,
studie`′ because they can a■
[4]
rminё
`o dltё
the poSitionS
Of hydFOgen (thOugh practica■ ■y deuteron). The fO■ ■Owing
structures were determined from X― ray and neutron p。
3)
diffraction by Sindor and his CO"orkと rs`8・ ■
"der
lPhase IIII
The low temperature forms in HCI and HBr and their
deuterium analogs are isomorphous.
Lattice: Orthorhombic, B-face-centered, with
lattice parameters as shown in table L-2.
space group' zvr- Bb2.,m.
"\?,
Number of formula units per unit ceIl z 4.
Atomic positions: All atoms in x, y, 0, with
x = a, y = 0 for the halog€trr and, as in
table L-2 for D
The origin used for this description is not the
conventional one given in the International Tables
for X-ray Crystallography; instead, it is chosen on
a mirror p1ane, midway between two b-glide planes.
In the y direction, where the choice is arbitrary,
it has been taken so as to make the y parameter of
the halogen atom zero
The structure is as shown in figure L-1. All atoms
lie at special positions on mirror planes. Taken by
themselves the halogen atoms form an all-face-centered
array, but the D atoms do not conform to this.
[5]
Lattice Parameters (in 10-10 m) and atomic Position
parameters of HCl, DCl, and DBr in phase III.
TABLE
I-2.
a
77。
4K
84 K
92。 4
92e4
Ｋ Ｋ
ａ ａ
DCl
ｔ ｔ
HC■
ａ ａ
DBr
ｔ ｔ
︻０︺
DC■
b
C
825
5.053
5。 373
5。
5.44
5.6■ 4
6.■ 20
5.082
5.4■ 0
5.826
5.069
5.399
5.829
XD
yD
08■
0.■ 70
neutron
0.075
0.■ 79
stud.y
0。
X-ray
study
PHASE IH
c蟹 ―Bb21
m
1-1. Arrangement of the molecules
in the unit cell of the ordered orthorhombic
phase III of HCl, IIBr, and their deuterium
FIGURE
analogs.
[7]
Each D is attached to one halogen, its donor,
■
and,
points towards another halogen, the acceptor of its
Cl-D...CI or Br-D...Br bond. The halogen atoms are
thus bonded in zLg-zag chains, with an angle of about
90o between bond.s, the chains extending parallel to
the y d.irection, with the y components of the Cl-D
or Br-D vectors all pointing in the same sense.
The similar array of infinite zLg-zag chains of
hfd.rogen bonds are also realized in hyd.rogen
gtuoriaeil4) The structure can be seen to be po1ar.
Each molecule is a dipole; since their y components
are a1l paralIel, the crystal has a net dipole moment
or spontaneous polarization. The structure as a
whole can be reversed by an electric field, and the
material is therefore ferroelectric.
There are three possible ways in which the structure
might reverse direction (i.e. .switchi-tg). (i) Each
molecule could change direction by 1800; this means
that the D atoms move from positions marked by small
open circles in figure 1-2 (a) to positions marked. by
(ii) Each molecule couLd change
crossed circles.
d.irection by 90o, movi-ng its D atoms fronn the small
open circles to the crossed circles of figure 1-2 (b).
(iii) Each D atom could. jrunp to a new position in its
bonds, again moving from the small open circles to
[81
Ｆ ｘ
VAV
〆ヽ〆
(C)
(b)
(a)
￨
――
A
A― A―
(d)
L-2. Structures of hyd.rogen halides.
Large open circles represent halogen atoms, and small
circles H or D, actual or average positions. Atoms
shown with heavy tine are at height 0, and those with
thin lines at height t/2. (a) , (b) , and (c) Effect
of switching the d,irection of the morecule through
180o fIip, 90" fIip, and, jumping processes,
respectively; the small crossed circles represent
the new position of H or D. (d) and (e) Relation of
the reversed chain at height 0 to the chain in the
origrinal direction at height r/2i corresponding to
(a) and, (b) and (c) respectively.
FIGURE
手
(e)
[9]
the crossed circles of figure 1-2 (c); it is thus
indistinguishable from (ii) in. its results. In no
case do the halogen atoms move, yet in (i) the position
of the chain has altered by a distance @/2 + b/2', ,
as shown in figure 1-2 (d), while in (ii) and (iii)
it has remai-ned unaltered, as shown in figure 1-2(e).
It is not known for certain which mechanism actualLy
occurs in ferroelectric reversal, but all three
posibilities are relevant when we consider what happens
at the transition.
As for DI, in contrast to DC1 and DBr, phase III
was found to be ordered monoclinic, space group
A
C:.
zn - C2/c, with 15 molecules in the unit cell.
The molecules form hydrogen bonded. squares stacked
along the monoclinic c-axis, the directions of the
bonds alternating in successive layers.
HI in
phase
III is not ferroelectric
IPhase II]
The structure of phase II,
which is missing in
HC1
and DCl, are isomorphous for HBr, HI, and their
deuterated analogs. It i.s still
orthorhombic, with
a unit, ceIl very nearly the same as in phase III,
containing 4 molecules, but it,s space group is now
1Q
o;; - Bbcm. The structure is shown in figure L-2(a),
争
[■
0]
PHASE H
Dll-
FIGURE
■n
■-3。
Bbcm
Arrangement of the molecules
phase II of HBr′
ana■ ogs.
´
[■ ■]
H工 ′
and their deuterium
４
８ “
〓 ０ ぃ＼Ｑ
ｍ︰
＞
嘱＼
∞
0く
L-4. Temperature dependence of the three
edglengths of the orthorhombic unit cel1, of the
unit cell volume and of the density of deuterium
bromide in the III-II transition region.
FIGURE
■
0
A=0。
■
nm
ψ
[■ 2]
if we allow smalL open and crossed circles both to
represent statisticaL half atoms. Each molecule has
two equilibrium orientations; one is the same as in
the ordered phase, the other gpposite to it. The atomic
position parameters, and the bond lengths are almost
exact,ly the same as in the low temperature form
The temperature dependence of the three celI parameters
over the III-II transition region of DBr was studied
The results are shown
by X-ray powder diffraction.
in figure L-4 together with the temperature dependence
of the unit ce1l volume and density. They suggest
that III-II transition is gradual. In phase III'
the thermal expansion along a has the greatest
anomalous increase, giving a large positive peak at
the transj-tion; that along c decreases, giving a fairly
large negative peak, while that along b has a small
but fairly sharp increase, Above the transition they
all have constant valuest o- = ob = 4 x I0 -a- K-1-'
0,c = -2 x 1o-4 K-1.
lPhase
Il
I' is the sane for
all the halides. It is cubic with space group
oi _ Fm3m (see figure 1-5). A detailed neutron
d.iffraction study of polycrystalline DCl at.111.5 K
The high temperature form, phase
子
[■ 3]
■
PHASE
●
o;
FttGURE
■-5.
of a■ ■
- Fm3m
The structure of phase
the halides.
[■ 4]
conclusively that the molecules were not
roLating, but that the average structure had its
D atoms distributed equally over twelve sites with
position parameters very close to those in phase III.
In phase I, the disordered models of 4-r 6-, and' 8fold., and random orientation or free rotation model
are all excluded. The ceIl parameters of HCI and
showed
DCI in phase I are shown in table 1-3.
It shows that
●
n
1-3. Lattice parameter (in 10-1-" m) and atomic
position parameters of HCI and DCI.
TABLE
XD
DC■
■■■.5
■■8。 5
■■8。 5
K
Ｋ Ｋ
DC■
ｔ ｔ
ａ ａ
HC■
at
5.47
5。
482
5。
475
[■ 5]
0。
■51
yD
0。 ■5■
neutron
stud.y
X-ray
study
゛
●・
the unit ceII of DCl is significantly smallerThis can be interpreted as the difference of the
effect of librational molecular motion. The thermal
amplitudes are consid.erably greater. In fact, D-Cl
bond length in phase r (1.l7 ;.), which is calculated
from the positional parameters of the atoms, is
considerably less than that of phase III . (L.ZS .i,).
The intermediate phase Ir of HBr was not investigated
by Sd.ndor. Natta claimed that the phase I' of HBr was
a face-centered cubic phase. Recent X-ray study by
/'r (\
simont"/ also reported it to be cubic.
studies by Hoshino
Single crystal diffraction
and his coworkers
lHcll
In 1969, some evidences for the existence of a new
phase I' of HCI between 98 and 120 K were discovered
from the single crystal X-ray and neutron diffraition
experiments by Hoshino et al{16-18) tn" structure
of phase I' was explained by a synthetic twin relation
of the orthorhombic lattice with the (101) plane as
the twin bound.ary. Possible average structure has
the space group ,iL - Bbmm or Dt P2L2L2L as shown
in figures 1-6 (a) and (b) , the former being the
as represented in f igures 1-2 (b) and'/or (c) .
[■
6]
same
)・・
■
.= t."、
.._
.^´
‐ ■
‐
:‐
￨ :二
^■
‐
1_■
^_
Ⅲ…
‐暉 出 綽 ‐ 越
一
‐ ‐ 議 ‐ 語 ■ヽ 3‐ ‐ 押 ニ ー 議 凛 ぶ ■ ‐
一
■ 豪
辞
一
゛
旗
●
D
1)
(之
■7
2h
Bblrm
φ
ｂ ｂ
FIGURE
■-6。
b
P: 二P217.7i
Two
for the phaSe
possib■ e aVerage
■'
of HC■
[■ 7]
.
strucfures
一
―
…
…
…
…
…
…
尋
.■
.,メ
‐
■r
However, neither structure can explain the observed
intensity
structure
structure
phase r t .
●
of
reflections. As far as the static
models are concerned, there are no posible
mod.els to explain the observed data in the
The dynamical structure models were thus
some
considered.
●
φ
ln the phase Ir the molecules may also form linear
zig-zag chains as in the ferroelectric phase.
As such chains are formed. at an instant, however,
they are d.estroyed at the next instant to form the
chains stretching in d.if ferent d.irections. The average
life time of the chain should be much longer than the
neutron passage time (ttO-13 s). Moreover, it was
assumed that the change of the direction of the chain
corresponds to the movement of the twin boundary by
means of the 90o flip of HCI molecules. The mechanism
of the movement of the twin boundary is shown in
figure L-7. The difference of the phase I and the phase
f is described by the difference of the length of
the hyd.rogen bonded zlg-zag chains and, the flipping
rate of molecules.
[DC■ ]
Neutron diffraction measurettents oF DC■
a s■ ng■ e crysta■ revea■ ed
(・ 9-子
2)using
that Such an anoma■ ous
[■ 8]
`
ｃ
パ﹂
６
L*,
fO-
"O
t'?t'
'tg
!?:｀
＼ Ｏτ
∝
気ひOo
B6d
＼
く
析
?
,,c9.
]--7. The mechani"sm of the movement
of the twin boundary by means of the 90o
f 1ip.
FIGURE
1o = (n/LBo) rad
lrsl
4,゛
●
t,ransition as observed in the higher temperature
cubic phase of HCI did not occur. However' disk-like
d.iffuse scatLering was recently found in DCl I below
L42 K at positions incommensurate with the cubic ceIl,
though it was not always observed and seemed to depend
on.the sample preparation. Sing1e crystals grown in
quartz containers sometimes show anomalous behavior
such as the transition observed at l-20 K in HCI.
These are explained thus to result from the influence
of external forces such as stress exerted by the
container wa1l on the crystal. Further, an investigation
of the phase transitions in both materials by neutron
scattering turned out to be unsuccessfuL largely due to
the experimental difficulties encountered. in the growth
of single crystals, their cooling down and their
passage through the transition without fracture of the
crystal.
on the other side, the rotational vibration (i.e.
libration) of DCI molecule was investigated. by analysing
anisotropic temperature factors of deuterium in the
powder neutron diffraction measurement by SAndor and
al?\
Farrow.'*-'
A similar analysj-s was developped by
Hoshino and his coworkers(19'21) using single crystal
diffraction data. Both results are shown in figure 1-8.
The mean angular displacements in and out of the (001)
も
[201
800
く
″
L卜 )、
０ ０
０ ０
６ ４
︵ ぃ０づ︶ ∩く∽〓
Ｎ
Tc
r′ m◆ p・
1f ;n)
\
PHASE
40
v
III
80
PHASE I
120
160
T/K
1-8. Temperature variation of mean square
angular displacements due to the molecular
libration of DCI.
FIGURE
キ
[2■ ]
plane are represented in the figure. .03ot> which
represents the molecular motion preventing the
development of zlg-zag chains in the plane (see figure 1)
9) increases rapidly above 123. K, whereas .Qirrt shows
no appreciable change with temperature. The temperature
variation of .O?rrt and .Q3rrtt correspond.s to that of
the probability for 90o and 600 flip motion of the
o
TJ
1-9. Twelve-fold. d.isordered. structure in the
phase I of DCl. In the phase III, the deuterium
atom of the cenLral molecule stays at the site I
and the central molecule is connected with both
left and right hand side molecules so that coplanar
FIGURE
zLg-zag chain format j-on is made.
l22J
=5LH“ 議濃饉盛餞藻L二 い漱
￨
―
・
・
・
轟 ―・‐
――‐
一
轟
―
molecule, respecti'reIy. The molecular motion was
also discussed from the NMR and NQR experiments as
will be reviewed below.
●
I-2-2. Infrared and Raman spectral studies
A completely unambiguous determination of the crystal
structure by spectral study is out of the question
but certain features of the structure can be obtained.
fn fact, before the neutron diffraction studies of
deuterium halides by SAndor et al., many workers
investigated Q3-26') for the positions of the hydrogen
atoms.
rg obseru"d.(27 ) trr" infrared
spectra of HC1, HBr, and HI in phase III and concluded
that tfre hcf and HBr crystals are built of zLg-zag
hydrogen-bonded chains. Savoie and Anderson
'(281 the infrared and Raman spectra of HCI,
remeasureo'
DCI, HBr, and DBr and suggested. the zig'zag chain to
be nonplanar, which is in contrast to planar one
j29)
study by rto
"t "f
indicated that the crystal structure of HCI, DCI' HBr,
and DBr in phase III is c)u - Pn2ra with four molecules
in a unit cell, and the nonplanarity of the chain is
d.etermined by S{ndor et al.
Raman
so smal1 that it is not sensitively reflected to the
spectra of lattice vibration region.
`年
[23]
・
:■ r暉 摯鴛螢彙壼識■・r,,'
correlation diagram for the proposed crystal
structure (Bb2rm) is shown in figure 1-10. It predicts
five infrared active lattice modes: three librational
The
modes (A.′ B.′ and B2)'nd tWO OptiCa■ transitions
(A,
and B, ) . Their mod.es of the two molecules in a
IL
primitive unit cell are shown in figure 1-11.
Raman study by lto et a1. also indicated two
(1) Rotational
characteristic features in phase III:
lattice vibrations have high frequencies in spite of
Molecule
Sitё
Factor
c OV
Cs
c2u
11
(T2),■
A2
ξttt
FICURE
s6■ id
■‐10.
phasё
Correlation diagram for
ITI.
[24]
Translational
Rotational
modes
mode s
ヽ
ごず
一 ヽ
Aぅ
、
、
｀
、
一
一
、
ン
一
一
ヽ
﹂
ヽ
ヽ
ヽ
tも
●
A.
,■
∼
｀
こ
チ
:イ
す
ピ
ヽ
)ヽ ト
‐
Bi
∼
ヽ二
‐
IB.
ヽ
ノ
:｀
オ
B2
:、 k〕
`fD―
Translational and rotational lattice
vibration of the two molecules in a primitive
unit ce■ ■ of hydrogen halide.
FttGURE
■―■■.
,
[25]
the weakness of the hyd,rogen bond. (2) The intensity
of the intermolecular vibrations is about 10 times
These were explained
stronger than that of libration.
?N\
by Hanamura'-"' as the effecLs of charge transfer
- (31)
on Raman scattering. Carlson and. Friedrich, measured'
the absolute absorption intensities of the infrared
active l-attice modes of HCI and HBr. It gave evidence
that the molecular d.ipole moments are less than their
gas-phase value as theoret.ically pred.icted by Hanamura.
The infrared and Raman spectral bandshapes of
internal vibration bands contain information about
molecular orientation and translational diffusion.
Raman study by wang et a1{32'33) ind.icated that
HCl molecules undergo rapid reorientation in cubic
phase at temperatures higher than L2O K, and satellite
peaks develop between 120 and 98.4 K suggesting the
evolution of a lower symmetry structure other than
the cubic.
There is one thing bothering. Infrared spectral
stud.ies by Hiebert and Hornig(34'35)
that
",rgg""ted
there are two adciitional phase transitions at about
25 and 10 K in phase III of Hf. However, present
calorimetric me.asurement showed no anomaly at both
temperatures as will be mentioned below.
T
■
チ
[26]
I-2-3.
Resonance studies
<h
The ""CI quadrupole spectra of HCl and DCI in phase
rrr were examined by Marram and n"gr"-(36) Activation
energies for both compounds were 2.70 1 0-05 kcal *ol-lt
in good agreement with values'obtained from dielectric
relaxation measurements by swenson and cot"(37)
(2.6 kcal mot-l) . The d.ata were d.iscussed in terms of
of mo1ecule. On the other hand'
the protot Tlp measurements by Genin et .rj38) g"rr"
the different activation energy of 1-4 kcal mol-I.
The data were interpreted as due to 90o flip motions
of the HCI molecules in solid III which, however,
are strongly attenuated in that they occur with
The fraction
nonequal site occupation probabilities.
some angular mot,ion
●
of the time that a molecule spends in the 90o posiLions
was found to be about 0.01 near the III-I transition.
Activation energy of 2.7 or 2.6 kcal mol-l was
i-nterpreted by o'neitty(39) to be a 1800 flip motion
of the molecule which occurs concurrently with the 90o
flip processes.
A single librational frequency was determined' by
okuma et a1{40) as a function of temperature from
35ct and 37ct NQR frequencies for HCI and DCI in phase
+1kca1mol*=
4。
■840
k」 mo■
[27]
・
.
●
III, the quasiharmonic treatment being used for
calculation. It does not fully account for Lhe
temperature dependence probably because of the effect
of intermolecular hyd.rogen bonds. Another interpretation
was given by o'Reilly(39) by means of an attenuated
90o flip process of the molecule mentioned. above.
A mechanism for the ferroelectric phase transition
in solid III of HCI is specified which j-nvolves the
90o as well as 1800 flips of moLecules.
In solid I of each hydrogen halide, two types of
molecular motion have been detected: (1) a rapid.
rotational reorientation and (2) translational diffusion
of the molecules. From the second. moment of the proton
and chlorine magnetic resonance, the structure of the
high temperature phase was proposed as being a hindered'
rotational one. An activation energy of 0.7 kcal mol-l
for rotation was derived by Okuma et al. The selfdiffusion of molecules below the melting point causes
narrowing of proton resonance line above 130 K' with
an activation energy of 5.6 kcal moI-I.
The activation energies obtained. by different
techniques and workers are summarized. in table L-4
together with the proposed processes.
128]
◆
●
﹁
一
一ト
．
ーーし ︱︰ＩＬ ＦＩ１１１，﹂
，
，
L-4. Activation energies obtained by NMR and NQR methods'
The values for deuterium compounds are shown in parentheses'
TABLE
-1
mol-t
substances E^/kcaL
o.
methods
workers
Processes
lPhase IIII
［ＮＯ］
HcI2.70+0.05?EMarramandRagle''some.angular
-'
] T,
-I of "tc1
Q964)
(2.70 + 0.05)
Genin et al'
TrO of H
L.4
(1968
HBr
(1.2)
(1970)
Hcl
(0.8)
(0.7)
molecule"
"rotation"
)
line width of 79g' Kabada et al.
tPhase
motion of
6
"
"g0o defect
motion"
Il
Tt of 35ct and D Powles and Rhodes
(1967)
"reorientation"
line width of 35cl okuma et aI'
(1968)
"rotation"
◆
●
IABLE I-4.
Continued.
mol-l
substances E^r/kcat
a.'
HC■
0。
worl<ers
methods
9
T■
p °f H }
Genin el a■
Tl of D
(0。 85】
(■
T. of H
4.4
［ωＯ］
5。
6
■ine
width Of H
T■
ρ
°f
H
966)
(■
。09〕
Tl of D
.
。
Gen■ n et a■
(■
(6.6)
T. Of H
(5.5)
line width of H
6.2
T.p of H
968)
Norr■ s et al.
〕
(■
968)¶
Genin et a■
"diffusion“
"diffusion"
968)
Cenin et a■
,
.
(■ 968)
HBr
t'rotation"
968)
Okuma et a■
(■
(3.9】
.
Krynicki et a■
(■
Processes
“diffusion"
"rotation"
"diffuslon"
.
"diffusttont:
(1968)
も
`
TABLE
■-4。
●
Continued.
r
mo1-1
substances E^/kcaL
a'
(0.97)
HI
methods
----r-^--lvorkers
Genin et a■ e
T. Of D
［ωＰ］
(■
6。
■
(■
Kabada′
P・
K., 0'Rei■ ■y′ D. E.
¶
Norris′
M。
0.: Strange′
J。
早.,
」.
“rOtation31
968)
Genin et a■ . ::diffusion"
T.ρ Of H
5
processes
Chern. Physe
P,W■ es′
」
・ G。
KryniCk土 ′ K. 」. Phys, C ■968′ ■′422, 445。
968)
■970′ 52′
2403,
, Rhodes, M。 , MarSden′ K.F
●
´
L-2-4. Dielectric measurements
Dielectric constant and loss measurements before .L957 t
(42-44) and
which were mainly carried out by Powres
cole and his coworkersjrz '45'49) t"t" summarized by
Cole and HavrifiariaT) Stat.ic d.ielectric constants
in logarithmic scale of hydrogen and deuterium halides
are plotted against t,emperature in figure I-12.
The activation energies from dielectric experiments
are shown in table 1-5.
Ferroelectricity of HCI and HBr in phase III was
discovered by Hoshino et aI. in 1967 j50) srrb""quent
measurement of spontaneous poralization from
pyroelectric current measurement in HCI by Kobayashi
et
showed. that, the maximum value of the
"ri51)
polarizatj-on is 3.64 pc cm-2, which can be compared
calculated by using the dipole moment
with 6.4 uC
"^-2
of HCl gas molecule. It was concluded that the d.ipole
moment of, HCl in crystal must be reduced to half the
value of free molecule. Sinilar measurement for HI
was not carried out by Hoshino et al. because of
They imagi.ned from the
experimental restrictions.
close resemblance of the nature of the thermal and
the dielectric properties to those of HBr that HI is
also ferroelectric in phase III. However, recent
studies of Hr by cichanowski tnd cole (49) gave no
[32]
T/K
FIGURE
L.Iz.
Temperature dependence of static
di-electric constants of hydrogen
deuterium halides
"
133l
and
_1.^嶋 _螢 ヵ山二_出 こぉ曇融純押盤■巌猿轟二ここ1
1-5. Activation energies obtained from dielectric
relaxation. The values for deuterium compounds are
shown in parentheses
TABLE
nu/kcai mol-I
substances
[PhaSe III]
HC■
2.6
HBr
2。
●
″
7
■.6
(1。
5)
(3。 6)
2.2
H工
(2.2)
IPhaSe ttI]
HBr
(■
HI
.5)
3。
6
(3.1)
[34]
.r
a!.*rh
-.*d
!
*ar; j;dr*rl.i!,
f-t4&,ltdFj'j;^:*
indication of ferroelectricity.
As far as that goes,
solid HI is not isostructural to HCl and HBr in phase
III as mentioned above.
a
L-2-5. Theoretical works on phase Lransitions
rn 1947, Tisza originally sugge"t"d (52) that the lower
IrI-II transition is due to the onset of disorder in
the d.ipolar direction while the molecular axes remain
para1le1. The upper II-I transition is then due to
a d.isord.ering of the molecular axes. It is further
suggested that III-II
transition is controlled by
dipolar forces and the II-I transition by dispersion
forces. Powles developed (53) these idea qualitatively
and semiquantitatively.
However, it was somewhat
the paucity of accurate measurements
and of the theoretical work available on the intermolecular forces in these materials. Among them,
the lack of neutron diffraction study was fatal.
In fact, the entropy of transitions was explained. from
the supposed structures, which are not identical to
those of SAndor et al.
rn Lg54, Krieger and James treated(54) the phase
transitions in hydrogen halides in terms of successive
rotati-onal or orientational transitions. . This model
consists of an arrav of classical rotators with
hampered both by
●
[35]
_,^“
=`丼
ェ ____=,_ニ ニ導出縁韓轟撫黙轟訟ふ=ヨしI___蘊 ‐●
nextneighbor coupling, the potential energy of
coupling being
S Oij)
E(O ij)= APl(cos Oij)+ BP2(C°
(■
)
where 0.r-l. is the anqle between the molecular axes of
●
symmetry. The model shows a single second-order
transition, a single first-order transition, two
f irst-order transitions, or a second.-order transitj-on
`
transition as temperature
rises. The modification of this modeL was developed
/cq\
by Kobayashi et aI.'""' in terms of a two-dimensional
rotational transrtion modeL with'two sublattices of
A and B. The potential energy is assumed to have
follorved by a first-order
the forrn
(BB)
Ｋ
i φ j)
＋
S(φ
(h)'°
４
３ 一
V=」
co,2∞
温鋤
￨―
%)(7)
where J and K represent the dipolar and quadrupolar
(or van der Waals) interactions, respectively.
/q6\
In 1970, Hanamura indicated\rv' that many properties
of molecules in molecuLar crystal-s of hydrogen halides
can be shown theoretically to deviate from those of
free molecules. The model proposed is that of zLg-zag
chain formation by a charge-transfer process of the fi
electron to the o* antibonding state of the neighboring
も
[36]
molecule. The strong Raman scattering due to
intermolecular vibrations as observed by Ito et aI.
can be explained.. The succeeditg p"p.t(57) showed
how essential the hyd.rogen bonding effects are in
phase transitions and how successive phase transitions
and ferroelectricity are induced by the intermolecular
interactions, i.e. dipole interactions, quadrupolar
interactions, and hydrogen bonding forces.
A thermodynamical explanation for the entropies of
the lower transitions of HCI, HBr' DCl, and DBr were
attempted by a"torr(58) assuming that the change in
librational frequencies at, the transitionsThis assumption, however, is not realisLic as shown in
the Raman sLud.y by rto et al . Qg) Anot'her analysis will
be requj-red.
■
[37]
*,-.t'.**.;*Itu.ilsu:&
t出
法〉
講
1-3. Purpose of the present investigation
t
As reviewed above, ever since the structures of
hydrogen halides were determined by neutron diffraction
●
studies, the phase transitionq were described as
those of orientational order-disorder type in connection
with Lhe molecular interactions. Nevertheless,
previous thermodlmamical considerations are not
sufficient tc elucidate the mechanism of the phase
transitions. One of the reasons may be found. in the
lack of the data with high accuracy and precision.
Since the earlier measurement of heat capacity, what
is worse still, did not extend below 15 K, the heat
capacity associated wj-th transition could not be
satisfactorily elucidated. A quantitative estimate
of the disorder present in the crystal- should be
mad,e from the anomalous part of heat capacity and
entropy. The analysis of thermodynamic results
therefore needs reexamination particularly now that.
the conflicting conclusions have been reached from
neutron diffraction experiments for the existence
of n'L20 K transition" in HCI. One of the aims of
this investigation is, therefore, to improve the
heat capacity data in terms of precision and of the
shape of anomalies in the transition regj-ons over
the previous works. Through the thermodynamical
●
[38]
analyses of the data obtained, our ultimate object
is to try to understand. the mechanism of
transitions in hydrogen halides.
●
●・
●
[39]
phase
…′,デ 墨ミ擦もふ
=.
`゛
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■.
●
」.
Timmerman′
■
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″ ‐ヽ ‐
一
轟
動
…
…
…
1燕経 ふ
一
…
(…‐
―
3■ 。 Car■ son′
…
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・
27′
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35. Hiebert′ G. L。 , Hornig′
●
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33。
26′
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」.
2794.
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ⅢⅢⅢⅢⅢⅢ 豪 辞結Ⅲ
・ ・
…
F.
0。
」。 Chem.
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Marram″ E. P:F Rag■
e′
J. L.
」b
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e′
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」e
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22′
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523。
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G. Nature
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G. J. Phys. Raditm
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Chem. Phys。
.
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:
46。
J
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23′
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Chem. Phys.
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2455。
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」ro
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」. Chё mo
Phys.
￨
49. cichanowski′ S. W., co■ e′ R. H.
」.
Chemo Phys.
1973′ 59′ 2420。
●
50。
Hoshino′ Se, Shimaoka′
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φ
5■
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52。
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G= J. Chemo Thermodynamics
[43]
■969′
■′ 24■ 。
CHAPTER 2
Experimental
「
[44]
1ヽ
■キ
,I総 喜
1■ ■
・ ・
,マ
2-L. Materials
HCI and DCI
HCl in steel bomb with a claimed purity of 99.0 mo1 per
cent was purchased from Matheson Co., Inc. After being
drj-ed in liquid, state over phosphorus pentoxide, it
was
distilled three times in vacuo. Solid HCI with redish
pink color was not observed, which had. been described
by Giauque and wiefejl) The final purity was 99.980
mo1 per cent as determined by the fractional melting
method during the calorimetry in the last series of the
measurements. Probable impurities are Hrr CL2r and
POC13, the last one being one of the prod'ucts of the
reaction of gaseous HCl with PZOS. The presence of H,
should affect the heat capacity of HCI at about 14 K
as seen j-n the resurts of ctusius12) who estimated the
amounts of H, from excess heat capacity. However'
present results showed no such ind.ication (see below).
Total amounts of specimen used for the calorimetric
measurements were determined to be (0.2025g + O-0002)
mol by p-v-T measurements using a calibrated volume of
the external gas-handting system. Non-ideality of HCI
gas was corrected for by the Berthelot equation with the
critical pressure of 8.26 MPa and. the critical
temperature of 324.7 KJ3) *n" uncertainty in sample
amounts arising from that of the critical constants is
145l
‐出に
線出碑軸
…轟 紳
““
轟
■ヽ
Ⅲ ―
・・‐ 串
・
・
…
“
優
｀
……
^…
i轟 議 枠
……
Ⅲ
…
…
Ⅲ
… …
'鶴
豪饗議中卜ⅢⅢら
4■ ￨
‐Ⅲ 轟
゛
"二 … … …
―
"・
not more than 0.01 Per cent.
DC1 gas was prepared by the reaction:
SiC・
4 + 2D2°
Si°
2 + 4DC■
(2-■
)
Conrnercial SiC14 and, DrO (Cna) with an isotopic purity
of gg.84 per cent were separately outgassed. and sicln
was transferred upon DZO. The reaction proceeded slowly
●
●
ln 24 hr. The DCl thus prepared was stored in the
gaseous state and subsequent purification procedures
were the same as those for Hcl. T'he purity was gg.g7 6
mo1 per cent. Amounts of specimen used were (0.21066 t
0.0002) mol, the critical
constants employed being
8.26 MPa and 323.5 KJ4)
HBr and DBr
HBr (Matheson Co., IItc., claimed purity 99.8 mol per
cent) was dried in liquid state'over phosphorus
pentoxide and distilled three times in vacuo'
The final purity was 99.987 mol per cent as determined'
by the fractional melting method. Total amounts of
specimen used for the calorimetric measurements were
determined by P-V-T measurements to be (0.19333 I 0.0002)
and (0.20466 I 0.0002) mo1 for Samples I and II,
respectively. Non-iddality of'HBr gas was corrected
for by the Berthelot equation witfr the critical pressure
[46]
`,―
い
■ II`、_・ ェ 二
,為 ―
ユ
・‐熟■t・ ヽ融 紳 ■::鶴線 た
・
i・
i・
● ■
●
・″ ““ =■ =■
=工
■■
■IⅢ _・ 年■“ゞ￨● なふ―
→￨●
‐や″
■
●あ■■
絲卿
中 「
・
…
… …
.ヽ
…
… …
…
…
l.“ ・
Ⅲ
・
, , ・
of 8.56 ltpa(5) and the critical temperature of 363.1
16\
K. to' The correction amounted to 0.8 per cent of the
total
amounts.
DBr gas for Sample I was purchased from Stohler Isotope
Chemicals. rts stated isotopic purity was 99 per centDBr for Samp1e II was prepared in the d'ark by the
'
reaction:
PBr3 + 3D2°
D3P°
二 十
3DBr
(2-2)
a stated isotopic purity of 99.84.
per cent. For both samples, purificaLion proced.ures
were the same as those for HBr and the purity was
DzO (Cna1 used had
99.g27 mo1 per cent. Amounts of specimen used were
(0.09653 t 0.0002) and (0-20535 + 0.0002) mol for
samples I and II respectiVely, the constants employed
being 8.56 Mpa and 362.0 Kj4) rrr" gases contaminated
stopcock gnease (silicone) of the external gas-handling
system.
Htt and DI
HI (Matheson Co., Inc., claimed purity 98.0 mol per
cent) was dried. in the liquid state over phosphorus
pentoxide and distilled three times in vacuo. The
final purity was 99.97 u mol per cent as determined
by the fractional (intermittent) melting method.
[47]
1 0'm― ●
Tota■
amounts of Specimen used fOr the ca■ or■ metric
study were determ■ ned by P¨ V“ T measurements tO be
●
(0。
■8904 上 0・
0002)mol.
Non―
ユdea■ ity
of HI gas was
corrected for by the Berthe■ ot equation w■ th the
cr■ tica■
8.40 MPa and the cr■ tica■
pressure o「 線
temperature of 424。 ■K∫
6)
Dtt gas was prepared in the dark by the reaction=
P + 5r + 4D2O ---t
●
D3PO4
+
(2-3)
5DI
(CEA)used lad a stated isotopic Purity of 99.84
per cent. Purュ ficatiOn procё dures Were the same as
D2°
those f6r HI and the purity was199.994 1no■
per cent.
Amounts of Specimё n used were (0.2■ 908
0002)mo■
± 0・
′
the critica■ constants emp■ oyed being 8。 40 MPa and
42■
8 K`4) The gas:￨: considerab■ y contaminated
。
stopcock grease (si■ iCone)of the externa■ gas― hand■ i,g
system.
t●
[48]
ri,t,M..口
、.人 `ttだ 二 碑
"轟
,メ ■ 楊
二 1轟1幕 1● L.… ∼■瀬 れ 靖 噺 風‐ 減 議 呼 よ
=Ⅲ
二 ‐ 赫 こ が ‐ 榊 品品 ‐ 躊 ■
鳥ⅢⅢⅢⅢ
“
…
“…
Ⅲヽ Ⅲ ●6゛ 鳳 哺 _Ⅲ 串 Ⅲ Ⅲ 申 Ⅲ
・
・
…
ヾ■
∼
■議れ‐ⅢⅢ赫‐‐‐
““
・
‐ ,ハ
‐ 4-“ ■ ■
■
“
2-2. Calorimeter
The cryostat and adiabatic calorimeter (gold) designed
for condensed. substances have been described previorr"fy!7)
A measuring circuitry including the automatic adiabatic
control system was the same as reported earlierjT)
except for the use of ar.rtomatic data acquisition system
for temperature measurements below 5 K. Both before and
after the whole series of measurements of HX and DX, the
`
●
heat capacity of the empty vessel was measured. below
300 K. The two independent measurements gave consistent
results, indicating that no permanent reaction such as
corrosion of the calorimeter had taken p1ace.
●
[49]
`
2-3. Temperature scales
The calorimeter is equipped with two thermometers,
a plat.inum resistance thermometer (Mod'el 8L64, Leeds &
Northrup Co.) to use above L4 K and' a germanium
resistance thermometer (cn-fOOO, CryoCal Inc.) to use
bel0w 14 K. We shall now describe their calibrations.
Platinum thermometer
ヽ
●
This thermometer was originally calibrated in 1966 by
the U. S. National Bureau of Standards based on the
IPTS-48 and NBS-55 temperature scales. The scale was
then converted to the rPTS-68i8) In order to check
for the aging effect during the eight years,
recalibratj-on was carried out in Lg74(9) against
the triple, boiling, and sublimation points t-H2, N€,
N2, 02, and CO, and also their vapor pressure scales.
However, fixed points of n-H, and CO, could not be
realized because of ortho-para conversion phenomenon
and insufficient heat lreatment, respectively.
The results shown in figure 2'L suggest, that the
platinum scale showed increases of 2n,3 mK in I year's
time between 14 and 90 K. However, it was ascertaj-ned
that the slope of the scale did not change appreciably
to such an extent as to affect the heat capacity values.
●
[50]
■
6
●
15
人→
人 Ｙ
Ｔ齢■ ○
■７０
5
○
唖
゛
ち
亀一
■
魃△
△
０ ５
ＸＥ ＼ Ъ ピ ー
［ｕＰ］
K
10
③
○
° Oo
0
― 10
― 15
0
20
40
60
8o
loo
戸/K
2-L. Calibration of the platinum Lhermometer based on 1PTS-68 against
triple (l) and boiling (I) points and vapor pressure thermometers.
A, n-Hr; A, Ne; o, N2t ot oZ.
FIGURE
Germanium thermomeler
4
`
The germanium scale was fixed by t'he 1958 -He vapor
A
--He
gas thermometr j-c
pressure scale below 4.2 K and the
temperature scale beLween 4.2 and 15 KJ9)
The following function *." o="U for fitting
the
calibration point,s by the method of least squares.
・
.0
Og・
01・
T(■
-4)
(2-4)
ill Ai・
The sca■ e cou■ d be determined to within +5 mK as shOwn
in figure 2-2。
HoweVer′ T5ё sca■ e was found to be ■ower
by ab9ut O.2 peF Cent at 4.2 K than therlnodynamttc
temperature sca■ e.
This disContinu■ ty is
with the one reported at the
■Oth
agreement
meeting 6f the comit6
Consu■ tatif de Thermomё trie (CCT)he■
0) ●
he
■
974∫
・
ュn
d in Paris in May
resu■ ting error in heat capacity did not
exceed O.5 per cent′ Which iS much sma■ ■er than 5 per
cent in this ternperature r9giOn as w■
[52]
■■ be
seen be■ ow.
一
一
い
2
Ｏ
気場＼睫
ｏ
06
06
0。
［いい］
︶ｄ ご 〇 一
ゆ
○
ι?Io
0
―
―
l。
o o _o_o_o _5.o
0
O
￨
二2
0‐
2146810121416
戸/K
_ 4,2-2. Calibration of the germanium thermometer based on TU, and -He gas
thermometer scales. The deviations f::om the scale obtai-ned by the method of
least squares are plotted. Two curves show the deviation of + 5 mK.
FIGURE
2-4. Heat capacitY measurements
The heat capacities of HCl and DCl were measured
between 2 and 164 K. The temperature increments were
about 0.3 K at the lowest temperatures and about I K
at IO K. These were increaseCi to about 2.5 K at higher
temperatures, except in the vicinity of transtitions of
HCl and DCl and near 120 K in HCl. Where vapor pressure
the temperature of the filling tube was
so adjusted that the calorimeter was the coldest in order
to prevent distillation of the specimen out of the
calorimeter. Thus, the top of the adiabatic shield
was made slightly warmer (up to 0.3 K) than the
calorimeter vessel. The resulting t,emperature drift'
due to heat leakage was taken into account in calculating
the heat capacity. This correction did. not usually
was significant,
exceed about 0.2 per cent of total heaL capacity
No helium gas was j.ntroduced into the calorimeter vessel
for heat exchange. Equilibration times after heating
were a few seconds at the lowest temperatures, 3 min
at 20 K, and 10 min at 80 K. About 80 K, except for
the transition regionsr'the sample vapor helped to
improve the equilibration time. The calorimeter vessel
contributed about 60 per cent of the total heat capacity
at all temperatures covered.
The heat capacities of HBr and DBr were measured
■
[54]
between 2 and
■90
Ko
about O.2 K at the
■O
at
K.
The temperature incrё ments Were
■oWest
temperatures and ab9ut
■
K
These were incrdased to about 2.5 K at higher
temperatures′ except in t,e v■ C■ n■ ty of trans■ tions`
Above 140 K′ Where vapor pressures were significant′
the fi■ ■ing tube ano a■ sO the t6p of the adiabatic
warmer than the calorimё ter
shie■ d were made s■ ight■ y
vesse■ in order to prevent disti■ ■ationo
No he■ ium
gas was introduced into the vesse■ for heat
The ca■ orimeter vesSe■
ёxchange.
contributed not more than about
60 per cent Of the t。 la■ heat Capacity for HBr and
DBr (Samp■ e
(Samp■ e ェ)′
工工)at
a■ ■ temperatures cOveredo
For DBr
the contribution increased up to abOut
75 per cent.
The heat capaCitiesi of Htt and DI were measured
between 2 and 225 K.
about O。 3 K at the
at
■O
K.
The temperature incrernents were
■owest
Thё Se were
temperatures and about
■ncreased
■
K
to about 2.5 K at highё r
temperatures′ except in the vicinity of trans■ liё nsO
Above 150 K where vapor pressures were significant′
the fi■ ■ing tube and a■ soithe tOp Of the adiabatic
shie■ d were made s■ ight■ y
warmer than the calorimetё r
vessel in order tb prevent diSti■ ■ati。 五。 No he■ ium
gas was
ュntroduced
into the vesse■
for heat exchangec
The calorimeter vesse■ contributed abOut 20 per cent
[55]
‐
to the total heat capacity at the lowest temperatures.
ft increased up to 60 per cent above 50 K except in
the vicinity of transitions.
●
[56]
む
2-5. Vapor Pressure measurements
The vapor pressures of, the solid in phase I and the
liquid were measured in conjunction with the heat
capacity measurements. A quartz Bourdon gage (Texas
rnstruments rnc., Moder 144-0i) was used for pressure
measurements. The gage was calibrated' against a mercury
manometer: The ratio of pressure value to gage reading
was a smooth function of the pressure to within 0.1
per cent up to 105 kPa. The mean density of mercury
at the temperature in a barometric column supported
by the pressure being measured. is given by reference 8.
The gravitational acceleration at our laboratory was
taken to be 9.79695 m s'2, whj-ch had been corrected. for
latitude and altitude from the value of g.79703?5 * "-2
at Osaka International Airport. The precision of
pressure measurements is $ Pa but the accuracy is
probably somewhat less than this because of undetectable
d.rift of nulI point.
[57]
■
2-6. Dilatometry
After measurements of heat capacity and. vapor pressure
for Sample II of HBr were concluded', an attempt was
made to determine the thermal expansion of solid HBr
by using helium gas as the dilatometric sensor between
65 and L2O K. The vo'lumes of the specimen and the
empty vessel were about 6 and 44 cm3, respectively'
The latter volume was separately measured as a function
of temperature after driving the specimen out of the
vessel. The equilibrium temperature and helium pressure
were measured at about 5 K intervals. To obtain the
maximum sensitivity, helium gas pressure was adjusted
to about, 100 kPa, some helium gas being wit'hdrawn
each time it tends to exceed the working range of the
Bourdon gage. Expansion of the helium gas and of the
vessel was subtracted from the measured. pressure
increment to compute the change of the specimen.
Since the precision of pressure measurement was 10
parts per million at 100 kPa, the smallest detectable
expansivity q is given
bY
cr-AT'(v/v) = 10 parts per. million,
(2-5)
where AT is the temperature increment, v the volume
of specimen, and V Lhe volume of helium gas. In the
present experiment, detectable limit. of cr, is estimated
t5Bl
●
to be 1.3 x t0-5 K-1. Since the expansivity of an
average molecular crystal is of the order of 10-4 K-l,
determination of the expansivity to two significant
figures was anticipated. by this experimental technique.
In fact, the volume changes "t afrt"" transitions of
HBr were observed. Quantitatively, however, expansivities
obtained were systematically amaller than those estimated
from densities by the X-ray diffraction
method.
The data obtained, therefore, will not be presented'.
origins of error are adsorption or desorption
of the helium gds, undetectable drift of null point
of the Bourdon gage, and inaccuracy of virial
coefficients of helium.
Supposed
0
[59]
REFERENCES to CHAPTER 2
ウ
■.
Giauque′ wo F。 , Wiebe′ R. 」. Ame Cheme Soc。
50′
■0■
■929′ 3′ 4■ 。
3. Gambi■ ■′ W. R. Chem. Eng.
■959′ 66′
4. Kopper′ =. Zo Physe 9hern・
A ■936′
5。
DroZdowski′
A
■9■ 3′
6. Woo■ sey′
亀
.
K. Z. Phys. Chem. B
2. C■ usius′
7. Atake′
T。
'■ 928′
E。
, Pietrzak′
」
` Bu■
■57.
175′ 469.:
■。 Acade
Crac.
239.
G。
」.
Am. Cheme soc.
■937.
59′
, Chihara′ H. Bu■ ■. Cheln. Soc.
■577.
」apan ■974′
47′ 2■ 26.
8。
The lnternationa■ Telnperature Sca■ e of
Metro■ Ogia
9。
■oo
chihara′
■969′ 5′
H。 , 工naba′
■968。
35.
A. Teion Kogaku
Mitsui′ K. Keiryo Kanri
[601
■975′
■975′ 24′ 36。
■0′ 84。
う
CHAPTER 3
Thermodynamic Properties
o
HCI and DCl
6
t 611
of
`
3-1. Heat capacitY
The experimental results without curvature corrections
are listed in chr6nological order j-n appendices 3A and
B for HCl and DCl, respectively. smoolhed values of
the heat capacity of the solids are given in table 3-1.
Strictly speaking, what was measured was the heat
capacity under the saturated vapor pressure, which is
Cs" However, the difference
between C= and Cn is negligibly smal1 because t'he
pressures are low j"n the measured temperature range.
Above 130 K, corrections for the vaporization of HCl
commonly denoted bY
iミ
or DCl, which occurred during the heat capacity
measurements' were significant (about 0.1 per cent
at 130 K). Quantities relevant for these corrections
were evaluated as follows. The vapor volume in the
calorimeter vessel Was calculated by using L.46g and
-- (1) at 107 K and
1.4S g cm-?J for the density of HCI\-/
at the triple point' respectively, and the liquid'
density oy xanaa.(2) Eensity of solid. an6 liquid nc1
was assumed to be larger by 3 per cent than that of
HCl on the basis of the X-ray diffraction data at
,r \
118.5 Kt5/ and the molecular weight. The heat capacity
(4)
oscopic a.t*
/2) R in the temperature rangie where the
values were required.. The total corrections amounted
is close to
(7
`
[62]
、
バ■
=せ
====■ ■==■ ■=■ _==二 0二
ユニ ●
1■
■
==燎
:“
=潔 ='4
capacity of -solid
at rounded va■ ues of temperatures"
TABLE 3二 ■.
The heat
Ｔ
一Ｋ
C
」k,■ m。 ■
'￨
HC■
￨￨
'DC■
0053
2
O.0052
O。
3
0.0■ 79
0。 0■
4
0.043
0。
044
5
0。
088
0。
090
6
0。
■6■
0.■ 67.
8
01429
0。
439
920
0。
944
80
■0
0。
■2
■1647
■。678
15
3.■ 0■
3.■ 33
20
5.980
6:0■ 14
25
8。
870
8。
956.
30
■■.54
■■.72
35
■3:89
■4.24
40
■5。
94
■6.54
45
■7.77
■8.65
50
■9。
43
20`163
55
20.98
22.5■ ‐
60
22.46
24`3■
[63]
‐
HCl and DC■
TABLE 3-■ .
Continued。
Ｔ
C
一Ｋ
゛
p
… 」K「 lmo■
=聾
∴
HC■
DC■
65
23.88
26.03
70
25.27
27.68
75
26。
80
28.■ 6
30.93
85
29:75
32.62
90
3■
.59
34`45
95
34.20
36.49
99
38.86
.45
44174
69
29。
30
■00
39。
■■0
4■
120
42.93
46e■ ■
■30
44.43
47.50
■40
46.04
48.94
■50
48。
00
50.80
■53
48.84
52.00
[64]
to at most about 3 per cent of the total input energy.
The results for HCI and DCl are shown in figures 3-1
and 3-2, respecLively. Both solid HCI and DCI have
A d'iscussion of
one isothermal phase transition.
other "transition" at 120 K in solid HCl will be given
below.
The measured heat capacities of solid HCI and DCl
´
are campared with earlier results in figures 3-3 and
3-4, respectively. The results are plotted as differences
from a smooth curve correspondi-ng to the values given
in table 3-1. The deviation of the present results from
t.he smooth curve, which indicates the precision, is {.5
per cent at the lowest temperatures, which decreases
to less than +0.5 per cent at 10 K' +0.1 per cent above
20 K, and *0.2 per cent at higher temperatures.
Giauque and Wiebe's results tor tiCl(5) are systematically
lower than the present results by about I per cent below
80 K, but the differences are within the combined limits
of error. Results of ctusius(6) are similar to those
Both results, however, were
of Eucken and x.t*ttj7)
fairly scattered and different from ours. Four results
agree well at about 20 and 90 K, which approximately
correspont to the temperatures of liquid hydrogen and
liquid air. Below 15 K, the results to be compared with
ours are onlv those of C1usius. Their results are in
[65]
r
戸/K
0
50
‐
100
150
200
60
15
Ｘ 、゛
３
ＴちＥ一
，
０
０
４
［ＱＯ］
Ｘ っ、 ゛
３
ＴちＥ 一
J
５
20
「
0
0
10
20
30
万/K
FIGURE 3-]二
Heat capacity of HC■
e
0
ご
戸/K
15
60
■ｏＥ ＴＹっ＼ ゛
HeOt CapaCity of DCl.
FIGURE 3-2。
I
万/K
0
30
‐
20
10
0
０
１ ５
０ ０
４ ２
J
七 ｆ 立 つ＼゛
・
［ぬく］
「
O
200
150
100
50
0
を
`
10
▲
▲
▲
V▽
▽
0
△
▽
▽ ▽
”・
Ｔ ｏｏ 凝
［６∞］
⊂ＯＯ﹂
①Ｑ＼、／Ｎ
一
5
°
T%十
十・▽
拳
V▽
t年
▼ ▽▲
▲
△
▽
▽
▽
▽選
+l■
々
▲
▽
▽
ぬ
▽ V
々 ▽
▽
▽
▲
▲
マ
十
▽
f +f '+ + 1 tt
△
十
▲
十
▽
℃
-5
fP。
0。
▲
△
0
― 10
0
50
100
150
戸/K
FIGURE 3-3.
reSultSF
△/peF
A comparison of heat capacity resu■
ts for so■ id HC■ . o′ present
5)A′
▽′ C■ usius∫ ,)+′ Giauque and Wiebさ ∫
Euckさ n and Karwat17)
C,nt=[CP(°
is given in tab■
,S.)TCP(SInoO,h)]X・
e 3二 ■.
09/に
p(SIn。
。 th)]′
Where CP(slnoOth)
◆´
゛
●
￨○
ず
。 ｆｏ
Ｐ ﹄藍 τ
ｏ
ｏ
0
●
0
-5
●
0。 0
O
い
［００］
樫 ①ｏ ３ Ｑ ＼ 甕
5
8
●0
・
0
・
●
∫
・
: :
0
°
●
0
●
。
●
0
●
0 .
●
●
。
。
。
●
.
0
●
●
●
0
―10
0
50
100
150
戸 /K
FIGURE 3-4.
A comparison 9f heat capacity resu■ ts f9r SO■ id DC■
.
o′
present
resu■ ts, o′ C■ usius and Wo■ f`8)
△/per
C,lt=に
p・
bS.),9p(SInooth)]X■
is gュ ven ュn tab■ e 3-■ .
00/1Cp(SInooth)]′
摯
ere cp(slnooth)
争
excess of our smoothed heat capacities by more than
20 per cent, which canlt be ploLted in figure 3-3.
It was explained. to come from 0'25 mol per cent of H,
as an impurityj6)
Heat capacities of DCl have'been measured above 15 K
fR)
by Clusius and Wolf .\"' A comparison of their results
with present results shows agreement in absolute value
only at. about 20 K. At other temperatures, however,
they are systematically lower than oot"l
A more sensitive comparison in the lower temperature
region can be made by use of equivalent Debye
temperature Oo, whose temperature dependence for 3Ne
degrees of freedom is shown in figures 3-5 and 3-6
■
for HCl and DCl, respectively. The Debye temperature
curves for HCl and DCI are almost superimposable below
about 25 K although the former is consistently higher
by a factor of 1.008, Above 25 K the DCl curve declines
more rapid1y.
じ
ft is probably significant to note that Clusius gave,
compared with ours, Larger values in the case of HC1 and
smaller values in the case of DCI.
t
●
[70]
,
″
奪
:50
ぴ”
Ｏ Ｏ
:40
O
Ｙ ＼ヾ
劇Ｐ］
［
130
▽
十
△
V VA
△
+
▽ ▲
JV
▽
▽
△
▽
▽
+
▽
120
△
▽
▽ ▽
▽
▽
▲
▽
l10
戸/K
FIGURE 3■ 5. The Dё bye characteristic‐ temperature Of HC■ dё rivё d from the
measured heat capac■ ties′ assum■ ng 3N degrees of freedom. o′ present resu■ ts,
7)
5)▲
6)+′
li c・
usius∫
diatque and Wiebe∫
′Eicken
and Karwat∫
薔
ρ
も
150
p。
0
∂6
Q
140
０ ０参ｏ
ｑＮ］
［
Ｘ＼ Ы
130
0
鬱
籍
e
e
e e
e e
120
e
‖
0
戸 /K
6"
characteristic temperature of DCI derived from the
measured. heat capacities, assuming 3N degrees of freedom. o, present results;
o, clusius ana wolrjS)
FIGURE 3-
The Debye
3-2. Vapor pressure
of the solid HCl and Dcl are
tabulated in the second column of tables 3-2 and 3-3,
respectively. The results were fitted to the Antoine
equation as follows by the method of least squares;
Measured vapor pressures
HC■
■o,10(P/Pa)
= ■9■ ■。3■ (K/T)+9・ ■875+0.0043■ 3(T/K)
DC■
◆
(3-■ )
■og.0(P/Pa)
= ―■079.74(K/T)十 ■■。5304-0.003896(T/K) (3-2)
Deviations from equations 3-1 and 3-2 are included in
tables 3-2 and 3-3, respectively. Fitting of the
results was also mad.e to equations of the form
A(K/T)+P
■
og.0(P/Pa)= ―
(3-3)
The resulting coefficients A and. B are given in table
3-4, vrhere they are compared with values reported by
others. A comparison with earlier results of solicl
HCl is shown plotted in figure 3-7 as differences from
equation 3-1. The difference probably arises not only
from the vapor pressure value but also from the
temperature scale used. Therefore, a comparison of
triple point pressure should be also referred to.
rn fact, Giauque and Wiebe's pressot"=(5) are
systematically higher than ours below the triple point,
■
[73]
TABLE 3-2.
VapOr pressures of HC■
P
P■ P(ё q。
kPa…
K
.
3-■ )
kpa
so■ id
■3■ 。983
O.7■ 3
0.002
459
0.976
-0。 00■
■37.■ 8■
■.366
-0。
002
873
■.88■
-0。
005
■42.540
2.562
-0.002
■45。 ■77
3。
442
0。
003
147.787
4.564
0。
008
■50.366
5。
969
0.006
■52.9■ 4
7.724
0.007
■55.392
9.862
0.0■ 9
■55.432
9.877
‐0。
005
■56.6■ 8
■■。080
0。
005
■57.402
■■.908
-0。
024
■57.794
■2.364
-0.0■ 8
■34。
●
■39。
Liqu■ 0
■60.600
■5。 744
■6■ 。040
■6.283
■62.9■ 3
■8。
■65.205
22.543
909
[74]
Vapor pressures of DCl.
TABLE 3… 3
PttP(ё O: 3‐ 2)
kPa
K
kPa
sO■ id
892
134.086
O。
■36.802
■。285
O.0■ 2
■39:485
■。786
0.023
■42。 ■25
2。
■44.738
3.■ 95
-0。 0■ 6
■47.3■ 4
4。 2■ 2
-0.025
■49.856
5.492
-0。
022
■52.355
7。
08■
0。
003
■53.052
7.584
0。
008
■54.876
8。
98■
-0。
044
155:2■ 4
9。
36■
‐o1043
156.782
■0。
764
-0。
020
■57.029
■■.089
0。
057
395
Liquid
■59.542
■3.832
■59.808
■4。
■6■ 。797｀
■64.039
'
058
■6.63■
■9.855
4
[75]
-0。 0■ ■
-0。
002
TABLE
●
3-4. CoefficienLs A and B for the vapor
pressure equation:
1oq"
-LU., (P/Pa)
=
-A (K/T) +B
B
A
HCl
Present work
●
Giauque anc wiebe
(1928)a
Karwat (1924)b
4424
■002.241
■0。
1011.46
10 26.gs
10.5068
10.6023
DCl
996.94
Present work
a From reference 5"
b From reference 9.
゛
[76]
■0.3929
心´
●
○.2
ｏｍｘ＼ ミ く
0。
￨
［﹃﹃］
一〇.￨
130
140
150
160
戸/K
A compar■ s9n Of Vapor pressure resu■ ts for so■ id Hc■・ 0′ present
■
■
9)O′
5)
)△ ′
at∫
三
ebe∫
▲
resu■ tsF +′ Giauque aha 轟
Henning and
Heng■ ein∫
´kaを 書
2)
Stock`・
△P = P(ObS。
)― P(SmOOth)
′ where P(smOoth)iS given by equation 3-■ 。
FIGURE 3-7.
whereas the■ r pressure at the trip■ e po■ nt iS
b
As a WhO■
(see tab■ e 3-6)。
Hc■
e′
■Ower
present resu■ ts fOr so■ id
are ■n aoreement W■ th th6se of Giauque and Wiebe
and Karwat∫
9)
As fOr so■ id DC■ ′the other measurement reported
■
ewiζ
near the trip■ e point is on■
■50
which is about
Pa
one
■arger 'than
by
ours.
et a■
・0)
.∫
ISotope effect
Of vapor pressure of the so■ ids may be represented by
●
the fo■ ■OW■ ng eqiation
■ed
from the type of equation 3-3.
も
■
og.0(Pic./PDC■ )〒
5。
30(K/T)+0。 0495
Lewis et a■ e gave fattr■ y different
■00.0(PHc./PDC■ )=
(3-4)
ёquation3
57。 7(K/T)+00387
(3-5)
Their resu■ ts on so■ id DC■ COnsist of 6n■ y four measured
points above
PHC■
■52
= PDC■ at
K and equatiOn 3-5 shows that
■49
K′ whereas our experimenta■
indicate that PHc.￨> Pbc■ aOOVe ■30 K. :
や
,
[78]
resu■ ts
●
3-3. Enthalpy of fusion and transition
The heats of fusion and. transition were measured in the
usual way of starting the heat input at a temperature
somewhat below the melting or.the transition temperature
and terminatin$ the input when the temperature had risen
somewhat above. A correction for the /Cnat was applied.
The results for fusion are given in table 3-5'
other measurements are also included for the sake of
comparison. In the series XIV both for HCl and for DCI,
the fusion was done in stages and measurements of the
equilibrium temperatures and pressures were determined
likewise. The results are given in table 3-6'
The triple points of pure HC1 and DC1, given as
(159.052 + 0.005) and (158.410 + 0.005) K, respectively,
were estimated from a plot of the equilibrium temperature
against the reciprocal of the fraction melted'
From this plot, amounts of a liquid-soluble solidj_nsoluble impurity were aLso estimated. The triple
poind pressure of DCl calculated. from the smoothed vapor
pressure is not in good agreement with the measured
Vapor pressures. In ej-ther event, however, Clusius and
wolfrs result is l0wer than ours. The results far
isothermal phase transitions are given in table 3-7.
The enthalpy of DCl obtained by clusius and wolf is
about 3 per cent smaller than ours. Entropies of the
[791
TABLE 3-5.
The entha■ py of fusion of HC■ and DC■
。
`
Seri es
T.
T2
no"
K
K
菫(Tう )― 早(T三 ).
△
平f
Jm。
■
」m。 ■
I
2■ 8■
.0
■970。 9
2■ 33。 6
■970。 0
Average
■970。 5
■
HC■
157。
402
XIVa
■57。
794
一 ¨
XIII
16■ 。040
■60。
620
b
Giauque and Wiebe (1928 )
■99■ .6
Eucken and Karwat (1g24)e
2■ ■0。 8
DC■
■56.782
XIVa
157.029
︼
¨
XIII
159.808
2■ 28.■
■944。 6
■59.542
2097。 6
1945。 3
Average
■945。 0
Clusius
and. Wolf '
`
[801
(L947f
■979。 9
tュ : ● ..、
_こ
.`￨´
‐
=ヽ
_●
…
ⅢⅢ ｀ 麟 取 ｀■
……
￨
.出
●ヽ一 ■`^^‐
``_、
_ニ
TABLE
ーー‐
"―
‐
`ヽ
‐
●
￨‐ ‐´‐●
―
｀‐
“
¨
ふ…
・
・
_`る ● ― ´ ‐●^“ ●¨ ‐ ●―
“
"″ ―
●
‐―
―
ヽヽ.“
^:^^..ヽ _・ ‐.′・
.｀
｀ ｀て
ル _● ,'ャ
・
… '‐_"_5■
― ス‐
― 轟
_■
●
^■
3-5. Continued.
`
a
b
c
d
rn this series, the fusion was done in stages'
From reference 5.
From reference 7.
From reference B.
ヽ
[8■ ]
―
-4‐
,A● ―・
―・ ヤ
軍 =● :"■
バ 黒 ■￨.1・ ■ ■、
`,
TABLE 3■ 6.
The trip■ e point 6f HC■ and DC■
Fraction
￨
T
P
HC■
344
158。 988
■3.82
0.6■ 9
■59.0■ 9
■3.87
0。
0。
●
757
895
(1 " 000)
0"
T- (pure HCI)
h
Rossini et al" (i952)*
liil-osavljevie (1949) c
clusius (1941-)d
159.022
159
"
■3.89
028
159 .030+o
13.90
.oo2
13 . B99a
159 .052+0.005
158.94
34
158.9
159
"
L3
.7gL
13.81-2+0.001
13.83
Eucken and Karwat (LgzAJf 159.
Karr.^rat
(:szug
159
[82]
.
34
13 .7 9
=:J11■
TABLE 3-6.
￨三
=,■
,1■ ■
1■ 空
■埜宝
=`摯
Ⅲ―
・す■1■ 1,生
■1■ 1■ 豊」■■
=酔・ 1…
｀
い
″Ⅲ ⅢⅢ中
輛
‐
・●
切 ‐ 1,
・‐
・ 撃 'Ⅲ …ⅢⅢ Ⅲヽ
∼
・
聖… ・
"'■
…
^ヽ
Contttnued。
Fraction
P
K
metrted
kPa
DC■
0.330
■53.325
l_2
0.598
■58.365
12 "60
0.8■ 3
■58。
377
L2.59
■58.380
12.59
0。
948
(1.000)
■58。
383+0。 002
Tr (pure Dcl)
■58.4■ 0+0.005
Clusius and Wolf (194?)h
■58.44
Lewis
a
b
c
q
e
f
g
h
i
et al.
(1934)
i
.50
L2.4784
■2.■ 7
■58。 2
The value obtained from srnooLhed vapor pressure equation.
Fron referenee
13
From reference 14.
From reference 6.
From reference 5Frorn ref eren ce
7.
From reference 9.
From reference 8.
Frcm reference 10.
[83]
iri,<+&!i4,u,rr..,,:1rr'!,allii$rrrr..,rl\:ia,r:'i'it,,),,j
TABLE 3-7:
r l:
,1:.:l
The entha■ py of transュ tiOn of Hc■ and DC■
Series
T.
T2
K
K
H(TJ)LH(T三 )
… …… …
」mo■
'￨
。
ギ (手 90)― H(97)
・
」mo■
HC■
a
工工
97.3■ 3
100.233
■295`5
■297.4
IIIa
97.062
■00.584
■3■ 7.2
■296.2
IV
97.3■ 0
■00。
330
■298。 7
■297.■
V
97.089
10■
.353
1347.3
■296。 4
Average
■296.8+0.6
●
Ttr
K
Present
wcrk
Giauque
and.
Eucken
Wiebe (1928ib
and Kanuat (Lg24)c
」mo■
98.67+0。 01
■■86.
98.36+0。 05
■■90.
98.75
■229.
Ross■ n■
et aI. (1952)d
98.38
C■ us■ us
(1929) e
98.9
[84〕
△Htr
・
TABLE 3-7。
Continued。
Series
T.
TL
no"
K
K
H(Tダ IH(T■
…
H(■ 06)一 H(■ 03)
)
… 」mo■ _1
」moir■
DC■
■03.309
■06.475
■500。 4
■5■ 4。 0
工工工
■03.■ 53
■05。
784
■500。 0
■5■ 4。 3
IVa
■02.574
■06.378
■547。 5
■5■ 3.5
V
■03.530
■05.920
■489.5
■5■ 4.6
Average
■5■ 4。
工工
a
●
β
△Htr
Ttr
」mo■
Present work
■04.63+0。 0■
■386.
Clusius and ?.Iolf $s47)f
■05.03
■339.
a rn this series, the transition was
I-\
c
A
u
e
*t
Frorn ref erence 5.
From reference 7.
From reference 13.
From reference 6.
From reference B.
185]
0+0.6
done
ユn
・
stages
"
■atent
heat part of transitions Werё determined tO
be(■ 2。 02+0.O■ )and(■ 312540:O■ )」
for HC■ and DC■
′ respective■
●
[86]
y.
K ・ mo■
―
■
や
″
3-4. 120 K transition in HC1
The heat capacity measurements of HC1 near 120 K
consistofthreeseries.Intheserieslandlll,
the temperature increments were about 1 Kt so as not
to overlook any small heaL anonaly' These were
increased to about 2-5 K in the series XIII'
In an attempt to determine the heat capacity of single
crystal HCI' the data (series I) shown by filled
circles in figure 3-10 were obtained after the following
heat treatment; the sample was solidified at 159 K
in 100 min, maintained' at L57 K for 4 htf and cooled
down to ll3 K at a rate of -0.03 K min-l, where the
measurements of heat capacities were conrmenced upwards'
The open circles (series III and xIII) in figure 3-8
are considered to correspond to the heat capacity of
polycrystalline sample because the sample was once
cooled. down below 98 K. The heat capacity curve is
smooth and continuous throughout the temperature range
between 98 K and the triple point and there is no
anomaly at or near LzO K. The supposedly single crystal
also gives essentially the same heat capacity as the
polycrystalline specimen. Both showed good agreement
with the results by Giauque and wiebe within the combined
limits of error. If we overlooked a small heat anomaly
at L2O K, its corresponding entropy would amount to
[87]
一・
●
52
４ ４
∞∞］
［
％
ｆ
○
２
％
4
Ⅱ
■ｏＥＬ っ＼ ゛
8
・、
40
100
120
140
160
戸/K
ё ′ sing■ e
in the parae■ ectric phase.
crysta■ ′ present reSultS, 0′ pO■ ycrysta■ line samp■ e′ present resu■ ts,
キ′Giauque and Wiさ be`5)
FttGURE 3=8,
Heat cOpacity oF solid Hc■
・ ■.二 島鵡働 _Ⅲ ⅢⅢ
¨
‐■■‐
‐
‐ 出― f議 ″
・‐ ・●
=鳳
・ ・
― ・・
…
￨
lt■ 0_
しK=■
m。 ■l
五
さ
re may be at 120 K′
'
壼
O aふb■ ify Whatever anoma■ y
さ
b■ Ot 6F‐ di士 :￨￨litii・ い
11
at most:
a
`二ёapacity is shown in figure 3-9.
l
One may thus safe■ y
conc■ ude that the l'transition" at ■20 K′ ■f any′
be seen by the heat capac■ ty measurements.
■
0
[89]
cantt
●
″
贅
［００］
誕 ＼ミ く＼゛ 超
Ｊ︰
ＬＯ
0.6
0。
4
。
0。
θ
00
2
TO.2
0
0 0
0
100
120
140
戸 /K
3- g. The differential
o, polycrystalline sample
FIGURE
heat capacity. o, single crystal;
160
functions
The thermodynamic functions of'HCl and DC1 were calculated
from the smoothed heat capacity values and other d'ata
described above. The contribution of the heat capacities
below the lowest temperature was estimated by a smooth
extraporation, which was negligibly smalt. The results
3-5.
`
Q
ThermodYnamic
are given in tables 3-B and 3-9 for HCI and DCl'
respectively. The entropy of liquid HC1 at triple point
was calculated to be 7 6.79 J K-1 mol-l, which is in
good agreement with 76.57 J K-l mol-I obtained by
Giauque and wieb.j5) The entropy of liquid Dcl at the
triple point, hovrever, was 81.02 J K-l *o1-1 in contrast
with 79.36 J K-l mol-l by clusius and worrj8)
This discrepancy arises from the difference in the
results of the heat capacity and"transition enthalpy
measurements as shown above
[9■ ]
TABLE
3-8. Thermodynamic functions of HCl.
Ｔ 一 Ｋ
so(r)-so'(0) {ir?(r):Ho(0I}yr -Ico(r)-Ho Q)}/r
-1
JK-t-mol.:
JK -1 MOl. -1
」K・
mo■・
so■ id
■0
0.274
O。 2■
2
0。
062
20
2.296
■。7■ 2
0。
584
30
5.793
4。
079
■.7■ 4
40
9.745
6.520
3.225
●
50
■3.69
60
■7.50
■0.80
6.705
70
2■
.18
■2.67
8。
80
24。
74
■4.42
■0.32
90
28.24
■6.■ 2
■2.■ 2
100
43.88
29.82
■4。
■■0
47.76
30。 8■
■6.95
■20
5■
.43
3■ 。76
■9。
■30
54.93
32.68
22.25
■40
58.28
33。
58
24.70
■50
6■
.52
34。
47
27.05
■59.0
64.40
8。
764
35.36
4。
925
5■ 2
06
67
29。
04
29。
04
Liquid
■59。 0
76.79
47.75
[92]
'..,..,,..pjj
TABLE
3-9. Thermodynamic functions of
so
K
(r) -so (o)
{.no.
(r).:go (o)
-t
.... ..Ji(.-tamo]--1l
JK-timoI..:....
DC1.
}/r rtco (r) .-Ho (o) } /T
jK ・ 轟6■
・
・
so■ id
064
■0
0.28■
O。 2■
20
2.329
■。735
0.594
30
5◆
866
4.■ 29
■。737
40
9.9■ 9
7
0。
6。
648
3。
9。
046
5。 0■ 4
27■
￨￨
50
■4.06
60
■8.■ 5
■■.29
70
22.■ 5
■3。
80
26。
06
■5.38
■0。
90
29。
90
■7.29
■2.6■
■00
33.75
■9.22
■4。
■■0
5■
.05
33.95
■71■ 0‐
■20
55.00
130 1
58。
■40
62.3■
36。
70
25。 6■
■50
65.75
37.58
28.■ 7
■58。 4
68.74
38.49
30。
74
34。
39
90
35。 8■
6。
863
8.763
68
53
20。 ■0
22。
93
25
Liquid
■58.4
8■
.02
50.77
Ⅲ
[93]
30.25
■二
■￨● ■ ￨■ .、 ■.,、 _、・、
￨■
…
…
認
縣
動
轟
凛
=Ⅲ _^、 ヽ
―
…
・― 一
―■. .^… … …^`_一
― ‐…
・ ヽ一‐‐― ●
“`∼ 一
‐4-―
‐ ″
¨… Ⅲ●■_.L__、 ■、1._…
´
￨■ ・ ‐
●
●
‐
′
●
_● ●●
・・・・
・ ‐‐
・'´ ‐″,ぉ ■
"、 た、__‐ .“
=…
… ^‐・
REFERENCES tO CHAPTER 3
C. Z. Phys.
■.
simon′ F., Vo Simson′
2。
Kanda′ E. Bu■ ■. cheme Soc:
■924′ 2■ ′ ■68.
」apan ■937′
3. Sindor′ E., Farrow′ R. F. Co Nature
■2′
473.
■7■ 。
■967′ 2■ 3′
4. P■ y■ er′ E. K。 , Tidwe■ ■′ E. D. Z. E■ ectrocheln。
■960′
64′ 7■ 7.
5。
Giauquё ′ W. F., Wiebe′ R.
50′
6。
￨
」.
Ame Chern: Soc.
■0■ 。
C■ usius′
K. Z. Phys. Chemo B
■929′ 3′ 4■
Clusius′
K。 , WO■ f′
.
■924′
7. EuCken′ A., Karwat′ Eo Z. Phys. Chem。
8。
■928′
■■2′
■947′ 2a′
G. Zo Naturforsch.
467。
495.
9. Karwat′ コ. Z: Physe Cheme ■924′ ■■2′ 486。
■0: LeWiS′ G. N。 , MaCDona■ d′ R= T。 , Schutz′ Po W。
Jo Ame Chelno Soё 。 ■934′ 56′ 495。
■■. Heng■ ein′ F. A. Z. PhySe
‐
■923′ ■8′ 64.
226.
■2.
Henning′
■3.
Rossini′ F. D., Wagman′ D. D., EvanS, W. H., Levine′
s。
■46
F。
, StOCk′ A. Z. Phys。 1192■
′ 4′
, 」affё ′ 工. NBS Cirё . ■952′ 500′ 549。
Mi■ OSav■ jeviё , D. M. G■ ashik Hem. DrOStVa BeOgrad
■949′
■4′
■3.
[94]
.
■
・ J′
´
■●与
・ ‐ 」= '・ ‐
“
,ヽ
Fヽ
=・
´´
●
ャ■
■
ユニ
メ冨 出饉出』 燿
‐
魔ェ 」
=二 ===ニ
=屁 ===“
=蔵
=よ ==■ ―
磁認濃嵩議
.■
=1:L総
`ム
ぶれ
`ぶ
墨L宦 五出 ユ蔵逸轟
=轟
(あ
:誌
Appendix 3A. Measured heat capacities of HCl.
玲
Ｔ 一Ｋ
T
…
」K
・mo■・
」K・
3K
mo■・
52.358
20.■ 5
Ser■ es 工
53.3■ 8
20.44
067
42.05
54.282
20。
■■5.065
42.20
55.250
2■ 。07
■■6.059
42.38
56.223
2■
■■7。
049
42.48
57.20■
2■ 。64
■■8。
035
42。 60
58:■ 77
2■ 。94
■■9。 0■ 6
42.87
59.■ 50
22。
■■9。
993
42.92
60.■ 29
22.44
■20。
968
42.95
6■ ◆■■8
22.82
62。 ■■6
23◆
05
34
■■4。
,
Cp
■2■ 。938
43。
■5
76
.35
20
■22.905
43.28
63:■ 27
23。
■23.868
43.49
64。 ■49
23.68
■24.829
43。 72
65.■ 85
23.92
273
24.22
67.4■ 5
24.54
572
24e86
69.734
25.23
904
25.53
■25。
786
■26.739
■27。
688
43.83
66。
44。 00
44.07
68。
Ser■ es II
5■
.390
■9。
70。
72.080
85
ヽ
195]
25。
86
遭■1餞 hヽ 義1●
^議"
jg:*:iif:::;l.f::gji,!lii:iu:itil:.:.r;:;-"f-i:;
::rd.ffiif;rX-,;:ji;!il*#Gt4r::.:---iij:-:J-!:-;ir5-j^l*l
Appendix 3A'. Continued.
0
Ｔ
一Ｋ
Ｔ 一 Ｋ
」K ・mo■
1
73.264
26.■ 7
■0■
457
26.53
■02。
75.65■
26.88
■04.■ ■3
76.847
27.23
■05。
74。
78。
044
27。
62
.426
608
770
■07。 4■ 3
J K -1 INOJ- -1
40。 2■
40。
38
40。 6■
40。
88
4■ 。09
β
79.44■
81。
035
27.98
28。
■09。
4■
.24
45
82.074
28.77
83.652
29。 3■
85.260
29。
86
80。
892
30。
39
8■
86。
042
Ser■ es II工
78。 7■ 7
230
.720
27◆
77
28.20
28。
66
88:535
3■ .■ 2
83。
90。 ■64
3■ ◆69
84.6■ 9
29。
38
86.237
30。 ■■
384
33。 ■6
87.828
30.72
94.973
34.35
89。
395
3■ 。28
96.539
36。 ■2
90。
948
3■ 。96
97.677
4■
9■
.780
93。
32。
92.529
.70
Transition
■00.575
078
40.■ 3
196]
29.■ 2
32。
65
64
93。
739
33.28
94。
549
33.80
Appendix 3A. Continued.
や
Ｔ
Ｔ
一Ｋ
一Ｋ
95。
363
34.48
■16。
JK-1*moI -1
42。
28
96。 ■72
35。
29
■■7.490
42.50
96.8■ 8
36.04
■■8。 5■ 7
42。
55
97.302
37.58
■■9.538
42。
84
97.77■
4■
.97
■20.555
42.90
98じ ■73
75.■ 6
.568
43.■ 7
■2■
Transition
■22.569
43。
21
■00.2■ 3
39.97
■23.552
43.49
■0■
40◆
09
■24.524
43.62
■02.380
40.33
■25.493
43.82
■03.774
40。
49
■26.456
44.00
62
40。
68
■27.432
44`04
■06.539
40.97
■28.5■ 9
44。
■08。
077
4■ .■ 4
■09。
775
4■ 。4■
.■ 3■
■05.■
‐
476
Cp
24
1い
11llll)
Series fV
■■■.293
4■
.64
Transition,
■■2.505
4■
.82
Continuous Heating
■■3.528
4■
.84
■■4.500
42。
03
■■5.482
42。
29
197]
¨
tJ・ ,絋・像 に,.=,一れ
=よ `よ I__■ ヽ一 ■“‐●●
“
Append.ix
3A. Continued.
●
Ｔ
Ｔ
Series
一Ｋ
一Ｋ
」K'・ mo■
Cち
…■
V
Transitionn
mol・
3.53■
0。
0303
3.946
0。
0430
364
0.0605
4.765
0.082■
4。
Continuous Heating
」K・
●
Ser■ es
VI
Ser■ es
VIII
2.067
O.00548
2.■ 28
O。
2.351
0。
00858
2.440
0.0■ 00
2.658
0。 0■
2.737
0。 0■
36
80
32
00607
0■ 4
0。
0■ 88
3。
043
0。 0■
3.4■ 2
0。
0270
3。
355
0。
825
0。
0360
3.668
0:0347
4.231
0.05■ 8
3.99■
0。
0456
4.6■ 3
0。
343
0。
0586
4.732
0◆
0784
3。
3。
Ser■ es
07■ 2
4。
0245
VII
2:■ 20
O.0060■
2.428
0.00952
2.760
0。 0■
3.■ 29
0。
Ser■ es IX
78
O。
046■
39
4.564
0。
0653
02■ 3
4.997
0。
0827
4‐
[981
.■
彙で 彙
■11‐1摯 ●■lr」■壼当 ■■蟻ょ
」
ルV,it,=お ど ●ヽ メ
'′
“
1■
Appendix 3Ao
_ 諄
■_■ ヽ
は
■■ ■■、
=´ “
==●
・ ==・ '■
===・
_ .^_.__… ■■■常 ^_■ 7,■■1■ ■■
Continued.
φ
Ｔ
Ｔ
一Ｋ
一Ｋ
...c.
---:T----=T
JK -mol :
.t1
5.49■
0.■ ■99
6.066
0◆
6.700
0.2352
7.429
0。
3377
8.280
0。
4845
JK-1-mol -1
220
2.■ 94
■4.339
2.75■
13。
■62■
Cp
Ser■ es XI
Ser■ es
6082
8。
884
O。
9。
630
0。 8■
■0。
446
■。0693
37
4.365
0。
0552
■■.359
■。3956
4.749
0。
0757
■2.342
■。7902
5.■ 88
0。
0959
■3.355
2124■
0.■ 403
■4.396
2。
744
3。
278
73■
5。
734
6.344
0。
7.0■ 0
0.27■ 0
■6.■ 68
3。
7.665
0,3648
■7.046
4。 2■
8.265
0。
4787
■7.96■
4.763
902
5.3■ 6
■948
i■
5。
3■ ■
0
0.6■ 94
■8。
623
0.8070
■9。 83■
■0.367
■。0433
■■.■ 84
1.3359
■2.■ 40
■。7008
8。 9■
9。
ser■ es
■4。
[99]
482
5。
■
864
XII
2。
846
=
Appendix 3A. Continued.
`
Ｔ
Ｔ
一Ｋ
一Ｋ
Cp
JK-1:mol-'1-
'r
JK- -moI -]
■5:478
3.368
36。
■6.466
3.883
37.489
■4。
453
38.6■ 5
■5。 4■ 2
864
■5.875
380
■4。 50■
964
■7。
423
4。
■8。
398
5.O■ 5
39。
■9.378
5.6■ 9
4■ ￨■ 34
■6。
20.382
6.■ 83
42.354
■6。 8■ 5
.428
6.787
43.609
■7。
257
492
7.4■ 0
44。
849
■7。
729
23.543
8.054
46.■ 07
■8.■ 42
47。 4■ ■
■8。
363
■
2■
22。
24。
592
8。
25。
650
9.235
48。
755
■9.023
26.728
9.805
50。
343
■9.542
808
■0.388
28.872
■0.942
29。
926
■■。520
■02.363
40.30
30。
975
■2.037
■05。 ■68
40.80
32.038
■2.547
■07。
625
4■ .■ 0
33.■ ■7
■3.044
■■0。
054
4■
34.■ 98
■3.525
■■2◆
608
4■ 。70
■■5.283
42。 ■4
27。
35。
285
■4。
628
583
Ser■ es X工 工工
009
[■
001
.48
卓
:Ⅲ
`潔 =織 摯
轟訥 熱
.… ■● 鳶 燻
、■___・
4蠣 曲 議 餞 離 爆 識 ■ 彙 議 彙 霊 彙 彗 壼 轟 彙 蓋 轟 =議
Appendix
饉轟畿癬議数彙肇壼藤綸
=晏
彙‐彙議轟‐轟轟曇饉壷議彙議密事蟷
=姜 ■
3A. Continued.
3
Ｔ
Ｔ
一Ｋ
一Ｋ
■■7。
925
42。
■20。
537
43.■ 0
mo■・
63
Series XttV
37
■23.■ 24
43。
■25.687
43.87
■28。
224
44.20
■30。
738
44.6■
■
」K・
■56.005
5■ 。35
206
56。 67
■57。
Fus■ on
)
■33。 22■
44。
95
■35.820
45。
32
■38.527
45。
86
.206
46.22
■43.858
46.60
■46。
482
47.20
■49。
077
47.77
■4■
■5■ 。640
48。
■54。 ■73
49.22
■56.4■ 7
5■
■6■
.756
58。 06
059
58.■ 5
■64。
49
.25
Fus■ On′
Continuous Heating
[■ 0■ ]
轟寮漱‐螢轟彙機彙競
=一
・子 ■1■
1“
=手 =￨■ 、運鸞盪
‐ 議二十■■‐‐■■Ⅲ=摯 ‐― ― ―
=な
_二
●
…
Appendix 38. Measured heat capacities of DCl.
◆
Ｔ
Ｔ
11… ￨
mo■ ■
JK「 聾
……
一Ｋ
一Ｋ
Cp
Cp
JI(-1 mOI -1
`
Ser■ es
76。 3■ ■
29.76
25
20.8■
77。
839
30.25
.560
2■ 。20
79。
393
30。
707
2■ 。63
52。
73
53.883
22。
09
55◆ ■■■
22。
56
76.98■
29.92
56.393
22.99
78:629
30。
57。 7■ 9
23。
50
80。
336
3■ 。03
59。
048
23。
97
82。
052
3■ :6■
60。
365
24.47
83。
779
‐ 323■ 9
697
24.92
85:489
32.82
63。
074
25。
37
87.223
33。
64。
486
25。
86
88。
994
34`■ 9
65。 9■ 0
26。
33
90.750
34.79
67.347
26.80
92。
68.82■
27.26
94.267
36.■ 6
70。 32■
27.79
96.032
36.92
7■ .8■ 9
28.27
97。
797
37.80
73.3■ 4
28`75
99.550
6■ 。
t::11111111)
29。
50.42■
5■
0
I
74.807
Ser■ es 工工
1■
02]
507
35。
38。
47
42
48
62
… 、_,==■ コ γ ^
=
=■
tt it_t,
Appendix 3Bo
Continued.
◆
■02。
973
C
」K ・ mo■
39。
4■
一Ｋ
.279
Ｔ
Ｔ 一一 Ｋ
■0■
i_ p
・
65
■0■
`78
Transition,
40.60
■03.65■
46。 ■0
Transition
■06。
￨
Ser■ es 工工工
.433
30`79
284
44。
22
■07.283
44.38
■08.278
44158
.38
■09。
268
44。
68
83.■ 15
3■ 。95
■■0。
256
44。
74
84.797
32。
8■
3■
45
■■■。240
44.86
493
33.■ 2
■12。 5■ 4
45。
06
88.■ 60
33.86
■■4。
266
45◆
34
Ser■ es
IV
86。
0
737
39.74
=570
■02。 627
Continuous Heatincr
79。
」K・ 轟o■・
849
34。
37
9■ 。59■
35。
09
93.348
35。
76
97.758
37.74
95。 ■20
36。
52
99。
600
38.70
37.28
■00.99■
39.33
03
■02.048
40.■ 3
89。
96。
894
98.33■
38。
99.422
38.50
■03。
090
4■
■00.502
39.09
■03。
985
50:99
[■
03]
.53
、■■ :^ 1■ _ 1_ 11^.し ,, _■
.:、
―ふ
…
「
■
_tt,二 ■ ■.こ 二審彙奮曇
_:
Appendix 38. Continued.
0
Ｔ
Ｃ
Ｔ
ｐ
一Ｋ
一Ｋ
」K
lmoir・
Transition
φ
■05.982
44.3■
Series
■06.873
44.27
Transition,
■07.86■
44。
Continuous Heating
48
■08。
844
44.64
■09。
824
44.64
V
Ser■ es
VI
■■0.898
44“
94
■。985
O。
005■ 6
■■2.■ 60
45.03
2.254
0。
00786
■■3。 6■ 0
45◆
■■5。
244
20
569
0。 0■
■■
2.886
0。 0■
63
2。
45.49
■89
0.02■ 9
97
′3.484
0:0286
3.787
0.0382
076
030446
■■6.940
45。
73
■■8.85■
45。
■20。
746
46。 2■
■22。
629
46。
3。
38
4。
■24.500
46.68
4:39■
0.0584
359
47.0■
4.764
0.0783
■28.205
47。 2■
5.■ 80
0.■ 055
037
47.42
■26◆
■30。
series VII
2。
■
[■
04]
05■
O。
00542
“
宅
‐
r
Appendix 3B.
Continued.
金
Ｔ
一Ｋ 一
Ｔ 一 Ｋ
2.322
0。
」K ・mo■
・
00840
Ser■ es
IX
655
0。 0■ ■7
2.968
0。 0■ 7■
3.280
0。
0228
4。
3.584
0。
0325
5.269
0.■ ■47
3.895
0。
0429
5。
720
0.■ 393
4.240
0。
0554
6。
242
0。
4.649
0。
0727
6.858
5.■ 34
0。 ■
2。
O.0649
4。 5■ 4
886
0。
0853
●
Ser■ es
038
0.2526
‐
7.6■ ■
VIII
■942
0:3662
Ser■ es
2.096
O。
00580
f4.340
0。
0500
2.382
0。
00920
4.696
0。
07■ 6
2.695
0.O■ 32
3◆ 0■
9
0◆ O■
5。
■00
1
0.097■
78
5.520
0。
■277
0。
■650
3.33■
0。
0247
5.996
3.635
0。
0306
6。
489
0.2■ 9■
3.949
0。
0438
7。
036
0.2865
303
0。
057■
7.7■ 3
4。
8.52■
[■
05]
1
0。
3945
0。
554■
Appendix 38. Continued.
●
Ｔ
Ｔ
一Ｋ
一Ｋ
iC p
l… …
」K=lmo■
「
9.393
■0.287
■■。236
0。
7575
■9。
」K ・mo■
565
・
5.763
■。043■
.■
Ser■ es
。377■
XII
■2.232
■。78■ 8
■4。 26■
2。
737
■3.244
2.226
■5。 ■65
3◆
247
273
2.732
■6.■ 2■
3.764
■7e■ 66
4e357
■8。 ■93
4.968
■4。
Ser■ es XI
393
0。
5069
■9.■ 29
5。
508
9.■ 9■
0。
7025
20。
062
6。
069
8。
003
0.9423
2■
■0.885
■。2448
2■ 。
■■◆849
■.6■ 6■
22。
899
7.733
■2.857
2.049
23。
872 /
8。
309
■3.86■
2.529
24.96■
8。
934
■4.806
3.053
26.■ 0■
9。
585
■0。
207
10。
995
743
3。
556
27.256
■6.672
4。
079
28。
■7。 60■
565
■5。
■8。
6.694
.040
.
7。
■98
408
■0.846
4.608
29.565
■■.473
5.■ 68
30。
734
■2.■ 09
`
[1061
Appendix 38. Continued.
●
Ｔ
一Ｋ
3■
.89■
33。
043
34.230
35。
452
■2。
705
■3.274
■3。
444
48。 23
■38。 ■43
48.73
805
49。 ■3
■43.43■
49.38
■35。
863
■40。
■4.459
36.677
■5。
042
■46.026
49。 87
37.9■ 3
■5。
607
■48.585
‐50。
39。 ■62
■6.■ 64
■5■ 。■06
5■ 。04
40.429
■6。 73■
■53.6■ 5
52。 68
4■ 。720
■7.288
■55。
829
55.2■
042
■7。
837
44.397
■8。
406
45.789
■8。
975
47.223
■9.535
48.654・
20.■ 2
■54.■
50.■ 45
20.64
■56:■ 2■
43。
47
Fus■ on′
Conti■ uou,
Heating
Ser■ es XttV
33
53。
54
60。 2■
Fus■ on
Ser■ es XttII
■27.8■ 3
47.■ 8
■30。
337
47.54
■32。
842
47。 9■
■60。
670
■62.9■ 8
●
[■
07]
6■
`■
■
6■ 。05
●
CHAPTER 4
Thermodyham■ c Properties Of
童Br
and DBr
●
l■
08]
‐
`
4-L. Heat capacitY
The measured. heat, capacity values are presented as
Cp in appendices 4A and B for HBr and DBr, respectively.
Curvature corrections were not applied, but may be
computed from the values since each series is results
of continuous measurements. The smoothed values at
rounded temperatures are given in table 4-1.
Above 140 K, corrections arising from vaporization
■
of HBr or DBr were significant. Relevant quantities
for such corrections were evaluated as follows'
The density of solid HBr in phase I was obtained from
the X-ray aata(I) at 120, 130, and 140 K, and' the
t2')
liquid density from Strunk and Wingate.'
Densities of DBr were assumed to be identical to those
of HBr. The heat capacity in the gaseous phase is
(7/2)R in the temperature range required'.
The results for HBr and DBr are plotted in figures
4-1 and 4-2, respectively. Solid HBr has three
transitions with a tail extending down to lower
temperatures. In contrast, solid DBr has two gradual
transitions. such an isotope effect is not seen in
other hydrogen halid,es.
The measured heat capacities of solid HBr and DBr
are compared, with earlier results in figures 4-3 and
4-4, respectively. The results are plotted as
`
[■ 09]
TABLE 4-■ .
`
The heat capacity Of oo■ id HBr and DBr
at rounded va■ ues of temperatures.
Ｔ
一Ｋ
Cpy
.
DBr
HBr
こ
・
―‐
■^^=.― ■
」K
mO■
O.0■ 56
2
O.O■ 5■
3
0。
4
0.■ 4■
5.
0。
6
0。
8
■.374
■:337
■0
2.634
2.634
■2
4。
262
4.■ 98
■5
6。
846
6◆
20
■0。
90
■0:90
25
■4.20
■4.34
30
■6。
75
■7。 ■2
35
■8.79
■9.46
40
20。
47
2■ 。56
45
22。
00
23。
43
50
23.46
25。
28
55
24。
98
27。 ■4
60
26。 7■
29。 2■
0.055
055
｀
0。
■38
296
0。
292
537
0。
533
[■
101
792
TABLE 4-■ .
Continued.
●
Ｔ
一Ｋ
(む
ヽ
.TK-ImoI
HBr
DBr
65
28。
68
3■ 。38
70
3■ 。■0
33.8■
75
34。 33
36。
80
39。
28
40.94
85
49。
80
47。
25
62。
55
90
80
95
4■ 。57
46e72
■00
43.67
47684
■■0
50。
50
53.56
■20
45。
09
■30
45。
24
■40
45。 8■
49。
■50
46.65
50.56
■60
47.69
5■
■70
48。
94
53。 ■2
■80
50。
62
57.67
49.■ 6
[■ ■■l
77
.58
●
戸 /K
100
0
100
50
200
150
25
80
20
●
￨￨
__
15
10
●
20
5
0
0
5
FIGURE 4-■ .
10
戸 /K
′
Heat capacity
[■
■2]
0
15′
ёf
HBr.
20
゛
Ｔ３Ｅ ＴＹつ＼
０ ０
６ ４
■ｏ
∫立っ＼゛
..●
n
戸/K
０ Ｆ
０
Ｏ
50
100
150
200
25
80
20
●
●
10
■
20
5
0
0
い
5
FttGURE 4=2。
10
ア /K
0
15
20
Heat capaむ ity of pЁ r.
31
[■ ■
1
゛
ＴｂＥ ＴＹつ ＼
０ ０
６ ４
゛
Ｅ
Ｔ３ ＴＹつ ＼
15
●
々
″
15
▲
ハ
AA
10
▲
▲
▲
▲
▲
▲
０ 会
０
5
O
▲
▲
ＯＪ戯Ｙ︶ｏ
十
十十
▲
十
_
ti^十
11+十
+1+
十
OT■
*l nJrr
♯
十
ヽ
-5
▲
▲
+
十▲
()8_
0
▲
▲
今
∠
▲
▲
▲
+
― 。
報
［ＰＰか］
ΦＱ＼ く
ｔｏｏ ﹂
▲
二10
=15 L
O
50
100
150
200
戸 /K
FIGURE 4-3。
resi■ tζ
0イ
′+′
A compar■ son of heat capac■ ty resu■ ts for solid HBr.
3)▲
Giauque ana Wiさ bё ∫ : Eucken and Karttat`4)
p9rC,nt=[CP"'S・
g■ ven
)「 CP(SInOOt,)]￨・
in tab■ e 4-■ 。
'9/rp(Sm?oth)]:Where cP(slnoOth)iS
o′ present
●
15
［ＰＨ ｕ］
＆ ＼く
ｔ８ ﹂
5
●
O
l. ..
. .
・:
0●
.。
r . :・
°Ч
「
番
:10.
●
_ ^ :
^
・。
1・・
.・
=・
-5
―10
―15
100
200
150
戸 /K
FIG▼ RE 4-4。
A compar■ son of heat capac■ ty results for so■ id DBre
resuitsF .′ c■ usius and wo■ f∫ 5)
) CP(Totり
￨:`;:I:in::[1:C:1:IS・
]文
・
09/に
p(SmOOtり
]′
where
o′
present
CP(smooth)iS
￨
differences from a smooth curve corresponding to the
values given in table 4-1. The scatter of our measured
points of solid HBr is 15 per cent at the lowest
temperatures, 10.5 per cent at 10 K, +0.1 per cent
K, and +0.2 per cent at higher temperaLures,
Near the transitions, it increased up to l-1 per cent
because of small temperature increments. since the
amounts of DBr in sample I are small, the scatter is
somewhat larger than that of HBr. For both HBr and
DBr, two samples gave id'entical results within the
extent of scatter except for two poinLs at about 2.5 K
in the series X of HBr sample I, which showed larger
values by some tens of per cent than the smooth heat
capacity. They obviously come from Poor manual control
of adiabatic condition at the lowest temperature.
Giauque and. wiebers results for HBr are in agreement
with the present results within the combined ljmits
of error. Eucken and Karwat's and clusius and wolfrs
results indicated the similar sltstematic deviations
as reported for HCI and DCI, respectivel-y
A more sensitive comparison in the lower Lemperature
region is mad.e by use of equivalent Debye temperature
above 20
°
Wh° Se temp,rature dependence for 3N degrees of
D′
freed.om
is shown in figures 4-5 and 4-6 for HBr and
DBr, respectivelY
う
[■ ■6]
100
0
0
中Ｈ劇］
［
ｘ ヽ ぬ０
90
十
▲▲
▲
今▲
80
▲
▲
70
30
戸/K
The Debye characteristic temperature of HBr der■ ved fFom
the measured heat capacitieS′ assuming 3N oegreeS Of freedom。 0′
present
4)
re6u■ ts, +′ Giauqte and "iebe∫ 3)▲ ′
Eucken and Karwat∫
Fェ GUttE
4-5。
●
L
■
0
roo
［ＰＰ∞ ］
ｙ ＼ ｏＳ
: :.3
o
ooo
90
●
80
●
●
70
T/K
4'6.
The Debye characteristic temperature of DBr derived from
the measured heat capacities, assuming 3N degrees of freedom. o, present
results; o, Clusius ana woftjS)
FIGURE
r4whEr!t+-!?"isiar+!*!rF&'.@..
.
.t'r4ek6iia@-*,
.
The Debye temperature curves for HBr and DBr are
almost superimposable below about 2O K although
the former is slightly l-ower near 8 and 12 K.
Above 22 K the DBr curve declines more rapidly.
●
[1■ 9]
‐ヽ ●
‐ ヽヽ
●‐■^● ―‐
´ "■
“_● ●
…
“
1
草
、、■、,●秦 ゛■
・●
・
・― ●
・“‐…
― ,■
"… …
"摯
●.―・0い 0"‐
●
…Ⅲ ―・
・●
―
●
・
t・
・
■9ⅢⅢ,■■■
“
"
.
ヽ
￨
=
…
‐
"…
・
`
4-2. Vapor pressure
of the solid and liquid HBr
(Sample I) and DBr (Sample Ir) are listed in tables
4-2 and 4-3, respect5.vely. The results were f itted to
the following equations by the method of least squaresi
Measured vapor pressures
HBr
1og10 @/Pa)
= -520.L4
DBr
(K/T') +3.92"19+0.01814 6 (T/K)
t":t:;:lrl
,.,,r, +6.8e45+0.
o0e8 s3
(r/Kt
(4-1)
(4-2)
Deviations from equations 4-1 and 4-2 are included in
tables 4-2 and 4-3, respectively. A comparison with
the resul-ts reported others is given in table 4-4The differences are appreciable:
Mcrntosh and Steele's
result"(6)
for example, 3t L77 Kt
show
a pressure
higher than ours by 9 kPa, Henglein's t""rrlt"(7)
a pressure lower by 70 Pa. The results of Bates et a1.,
which consist of only 3 points for both solids, indicate
no isotope effect in contrast to present resultsThe equations 4-L and, 4-2 ind.icate that a plot of
log P against t-l has such a slope that increases
at higher temperatures. One of possibilities that
might give such an effect would be decomposition of
hydrogen bromide,to rel-ease some hydrogen in the vapor
phase. However, there were no ind.icatiOns of decomposition
[■
201
fABLE
4-2. Vapor pressures of IIBr.
P"P(eq. 4-■ )
kPa
kPa
K
So■ id
023
506
■.6■ 9
■53。 0■ 8
2。 0■ 9
-0。 00■
■55。 5■ 2
2。
52■
-0。 02■
■58。 0■ 7
3。 ■54
-0。
034
■60.507
3。
943
-0。
036
■62.976
4.915
■50。
0。
-0.025
004
423
6。
■04
0。
■65。 432
6。
■22
0。 0■ 7
■67。
865
7。
558
0.052
■70。
304
9。
250
0。
045
■72。 72■
■■.300
0。
064
■75。 ■43
■3.76■
0◆
077
■77.518
■6.5■ 3
二0。
046
■79。
866
20.002
10。
054
■79。
869
20。 0■ 2
0◆
059
.907
23.352
-0。
057
■65。
■8■
■83。 9■ 9
27。
304
-0。
059
■84.262
28。 ■40
0。
043
■85。
595
30.975
-0。 ■5■
■85。
605
3■
.079
-0.07■
[■
21]
TABLE 4■ 2`
Continued。
始
P
P-P
kPa
l
Liqtid・
り
■87.360
34。 500
■87.449
34`906
■89:27■
38。 865
■89。
363
39.342
■89。
375
39。 380
■9■ .24■
44.244
0フ
[■
22]
・
(eq. 4-1)
‐
kPa
■よ ■ 凛
i‐ ハ
‐
二
凛
一
TABLE
4-3. Vapor Pressures of
DBr.
贅
P-P
kPa
kPa
K
(eq. 4-2)
So■ id
■56。
●
027
2。
494
0。
007
■58.498
3。 ■5‐ 3
=0。 00■
■60.949
3.959
-0。 0■ 0
■63.383
4.946
‐0。 0■ 5
■65。
844
6`■ 78
-0。
007
■68。
326
7。
695
0。
007
■70.828
9。
556
0。
027
■73.347
■■。798
0。
025
879
■4。 5■ 8
0。
02■
■78:437
■7。 74■
■8■ 。037
2■ .9■ 4
0。
049
300
26。 0■ 2
-0。
037
●
■75。
■83。
Liquid
■86。 88■
33。
439
中
[■ 23]
-0.07■
1｀
■^‐ ｀
｀ ´
ご -1.
・
凛凛‐
「
ニー
´
:
…￨
■・
: ￨
‐
TABLE 4-4。 Coefficiё nts A land B for the ,apor
pressure equation3
●
・
1
1´ .￨
A(K/T)十 B
°g■ 0(P/Pa)= ¨
￨‐
‐‐
A
B
HBr
■035。 ■2
Present work
1103
et al. (L935)a
1138.6
Hengrein (1923)b
807
Mcrntosh and Steele (1906)c
Bates
●
■0。
0556
L0.434
10.63L
8.92
DBr
Present work
Bates
a
b
c
et al.
(1935)a
From reference 8.
From referen ce 7.- From reference
6-.
Ⅲ
[■
24]
2457
1069:80
■0。
■103
■0.43■
1 1
in the temperature drift of heat capacitl'determinations
nor in the purity determination at the triple point
which was conducted aft,er alL the vapor pressure
-
●
measurements had been concluded-
o
-a
ウ
1125]
LJ
●
‐
嗜
4-3. Enthalpy of fusion
The results for fusion experiments are given in
table 4-5. A correction for the .fCndT was applied
to compute the enthalpy of fusion AH, from cumulative
enthalpy H(T2)-tt(Tf ). t'leasurements by other workers
are also included for the sake of comparison.
The mean values of the enthalpy of fusion of HBr and
DBr obtained \^/ere (2398.7 + 1.0) and (2369 + 4\ J mol-l,
respectively. The rather J-arge uncertainty in DBr
comes from smallness of amount of specimen used' as
Samp1e I.
The triple points of pure HBr and DBr, given as
(I86.500 + 0.004) and (185.64 + 0.01-) K respectively,
were estimated from a plot of the equilibrium
temperature against the reciprocal of the fraction
melt,ed (see table 4-6). Although the melting was
broader in DBr because of larger amount of impurities,
this plot was approximately linear.
今
[■
26]
The entha■ py Of fusiOn of HBr and DBr.
TABLE 4-5。
`
Sample
Series
T.
T2
no.
K
K
H(T2) H(T.)
」mo■ ―
△Hf
Jmo■・
HBr
工
Ｉ Ｉ エ
XXIII
■85.595
-
■87.360
2502。 ■
2398。 9
XXIVA
■85.605
-
■87.449
2505。 4
2397。 7
rva
■86。
099 -
■88.478
2538.4
2399。 4
●
Average
●
2398。
Giauque and, Wiebe (le28) b
2406
Eucken and Karwat $s24\c
2594
7 +
DBr
エ
Ｉ Ｉ Ｉ
XIIIA
■82。
593
■86。
762
26■ 6。 0
2369
XIV
■82。
790
■86。
585
2590:4
2365
rxa
■83.300
■86.88■
2579。 9
2372
Average
CLusius and Wotf (1947)d
[■
27]
2369 +4
2403
■。0
TABLE 4-5。
Continued。
a In this series, the fusion
b From'reference 3.
c From reference 4.
d From reference 5.
0
1■
28]
was done
in stages.
TABLE 4-6.
The trip■
e point of HBr O,o Dpre
Fraction
Samp1e
kPa
melted
HBr
186.415
L86.453
L86.467 :
18 6.47 6
18 6.482
186.484' + 0.002
0.134
0.319
0.504
r
●
0.588 '
a.874
(L. o0o)
0。 245
ェ■
1
1
1
■86.440
1
03464
■86。 462
111
0.684
■86:477
・
0.902
‐ ■86.483
000)
1(■ 。
.
32-79
32-88
32.98
33.03
33.10
33 - 3La
1
‐
■861484=三 90002
L86.500 ! 0-004
Tg (pure Hgr)
Giauque and, wiebe (1928)b 186.24 ! 0.05
(Lgz[c
clusius and wol,f (1947)d
Eucken and Karwat
[■
291
187.0
33.L
TABLE 4-6e
Continued.
●
Fraction
Sample
kPa
melted
DBr
25■
■85.269
0.376
■85.4■ 4
0.495
■85。
O。
エ
0.609
■85.49■
‐
0。
735
■85.505
0。
89■
■85。 528
(■
II
450
1
■85.548 ±
。000)
0。
005
300
■85。 343
30。 ■6
0e56■
■85:474
30。
9
■85.527
30.96
0。
0。 8■
(■
73
■851548 + 0:ё 05 1 30:9■
.000)
185.64 !
Tf (pure DBr)
cLusius and wolf (1947)d L85.62
0-01
30-9
a
The va■ ue obta■ ned from smoothed vapor pressure
b From reference 3。
・
C
From reference 4。
d From lと ference 5。
￨
[■
30]
a
‐
‐
■ ￨
ёquatione
●
4-4. Transitions in solids
Details of thermal behavior of a phase transition
by the enthalpy change through the
transition region. Figure 4-7. refers to the transition
between phase III and II and figure 4-8 to that between
may be manifested
II and I incLuding phase Ir of HBr.
The different series of results were normalized on
the high temperature side of transitions. The transition
temperatures were then determined from the point at
which the rate .of change of enthalpy with temperature
is a maximum.
In the lower transition of HBr or DBr, the time
to reach equilibrium after heating r^tas off became
an hour or more. At each such point, the rate of
change of temperature with time was followed for 40
min, the results fitted to a first-order rate 1aw,
and the equilibrium temperature (T-) obtained by
extraporation. The temperatures plotted were determined'
in this way. In HBr, the time required to come within.
0.001 K of Too v/as about 40 min. Transitions were found
to be continuous.
The upSrer two transitions of HBr obviously differ
from each other in equilibration time. On the low
temperature side of the transition at 113-60 K it
requires a very long timet In fact, the time required,
phase
t
[■ 3■
]
S
▲
ハ
26
２ ２
２
４ ・
Ｋｒミ ︸
Ｏｒミ ︲︵
Ｔ３Ｅ っＸ ＼ 一︵
Ｐωヽ中
［
2。
0
L8
86
88
‐
90
92
94
96
π /K
Entha■ py change
■n the reg■On phase II工 → phase ttl of HBr and DBr。
The different series of measurements are
■orma■ ized on the high temperature
Side Of transitions. HBr Samp■ e 工8 [0, (工 ), Δ′ (XIII)]. HBr Samp■ e 工工8
FttGURE 4-7。
▽′
(II).
DBr Sample
工8 [● ′
(VI),
▲′
(VII)].
4.8
●
44
０
４
Ｏｙミ Ｌ︵
ｋｙミ ︸
一＼ ︷＾
ＴちＥ っ
,
3.6
3.2
￨10
H4
´
H8
122
‐
I
FIGURE 4-8` Entha■ py change in the reg■ 9n Phase 平
phaSe =
=.→
of HBr and DBro The different ser■ es of mё asurements are
1
●
万
/K
nbrma■ ized on the high tempeFature side.of transitions.
HBr Samp■ e 工= [o′ (X工 V), △′ (XV)′ ▽′ (XVI)]. 軍Br samp■ e ==:
口
' (=I■
):
DBr Samp■ e
エ
= [● ′ (vIエ )′
工
[133]
▲,
(lX)]`
￨
ウ
ёstimatё d
ecomes O.Oo■ K was
unti■ T― T∞
5 hr frOm the observation during an hour
■■7100
to 20 min in the transition at
Ke
to be about
■n
contrast i
‐
The uppeF
trans■ tion of DBr ■S a discontinuous one with a ta■ ■ ￨ ‐ ￨
to
■ower
The ca■ orimetric studies
telnperature sideo
‐
‐
of the trans■ tions are′ bowever′ cOmplicated by the
occurrencさ of hysterё sisl?)becouse thё geometFy of l
ca■ orimeter
vesse■ and the methOd 6fl heating ■nevitab■ y
cause non― uniform heating Of the Specェ mё ,: Thё refOrer
●
therO is some ambiguity
ュn
‐
‐
the brder or type Of tr● ns■ ￨■ 9ni
￨
t6 be specified‐ by the eXperimenta■ reSu■ ts。
The entha■ py cha■geS Ofl lhe tFanS■ tions measured are
‐
shown in tab■ es 4-7 and 4-8 fbr I11-ll and II― I
tranSitiOns, rё SpeCtiVe■ y・
Of HBF′
△Htr
C° u■ d b9 unambiO●
of its sharpnesso
‐
In the transition at l■ 7100 K
Ous■ y est■ mated oeCau,01
lt iS 415 per Centisma■ ■er tha, ￨ ￨・
the va■ ue of Ciatquё and wiebぎ
6
[■
34]
3) ●‐ ￨
￨‐
￨
‐ ‐￨
"-:.,...--.
--*.-.'-rr4lhq"\.'th.
4-7. The enthalpy of transitions between phase III
and II of HBr and DBr including the "normal" part of
TABLE
●
heat capacity.
samp■ e SerieS上
no.
上
K
K
弩
ざ
嬰
1型
牲
写
事
里
HBr
r
r
rr
rr
ra
88.266 90.702 399.0
xrrra 88.506 90.308 365.2
88 .955 90.089 315.9
r
88.7L4 gr,'.lgL 367.3
rra
Ave=,ge
373.2
373.5
372.L
372.0
372.7
主
008
Ttr
Present w6rk
GiauquO and Wiebe (■ 928)b
Euckei and Karwat (■ 924)C
ド
リ
、
1■
35]
89。 ,3 ± 0。 0■
‐
89。 2
‐90
‐
TABLE 4-7。
Continued.
●
T2 11(T2)
-H (rt)
.7T-T
TK
.fmol
Series T,
Sample
+
no.
K
H
(9a.5) -H (92'.5,
JmoI
DBT
r
r
r
r
O.
vra 92.450 94.760 402.7
vrra 92.678 94.387 363.5
vrrr 91.823- - 94 .265 42g .7
rx
90.821 - 94.405 511.0
Averlge
3g5.7
384.9
384.2
385.4
385。 ■ ± 0.9
'FE,r
Present
. 93.6'1 + 0.0L
work
A
Clusius and WoIf (1947)*
a rn this series, the transition
b
From reference
c
d
From ref,erence 4.
From reference
3
5
[136]
was d,one
93.5
in stages.
4-8. The enthalpy of transitions between phase II
and I of HBr and DBr incLuding the t'normal" part of
heat capacity.
TABLE
´
●
坤
p・
e
Series
no.
f
T Jm。
T.
I T2
K
HBr (エ・エ
I
XXI
simple
'9ri'S
'(Tう
工)
)`耳
(T.) H(1■ 1)IH(■ ■3)
moi=・
・
.―
￨
■■3。 ■43 ‐ ■■8。 ■65
:」
:
855`■
855`4
■
no.―
T2
_T・
K:I T‐
HBr (II-I|
t｀
1lilD
r
r
r
r
rr
H(T2)=H(Ti) H(■ ■5.5)THll113)
Jm6■
」mO■ ll
=・
)
xrva L12.508 1L5.344 404.9
xva 113.L85
)ffrr 113.152 115.289 366.7
xx LL2.g67 115.366 380.1
rrra 113.041 - LL5.725 395.7
AverOge
385.9
386.I
385.4
386.
O
385。 7 上
0・
4
Ttr
Present work
‐
■■3.60
壼
Giauquё and wiebO (■ 9'8)PI
[137]
■
13。 4
+ 0。 0■
TABLE 4-8`
Samp■
e
Continued。
Series
no.
T.
T2
T
ず
K
H(T2)二 H`Tl),(l18),H(■ 1'05)
」・
m。 .―
‐ 品■
「11
HBr (I r -I)
●
f
r
r
r
r
rr
xrva 115.344 ].Ll.466 453.7
xvra 115.704 - 1L7.g23 455.3
xvrrr 116.710 I17.491 390.3
xrx
LL6.273 LL7.745 4L5.6
rrra l:-s .725 - LL7.733 445.5
469.6
469.4
469.5
46g.g
469
.3
Average ' 469.3
k‐ ￨￨‐
Present work
■■7100 +‐ o.o■
Ciauque and Wiebe (11う 0)b
■■6:8
[■
381
0・
5
△
Hti
Ttr
￨●
上
温
il■
343
‐ ‐ 359
‐
TABLE 4-8。
Sample
Continued。
Series
T2
T■
no.
T
K
DBr
●′
●
H(T2) H(・
」
moi―
・
.)
H(■ 2■ )― H(■ ■8)
Jmo■
￨
・
I)
(II―
I
VITIA
■■7。
I
rxa
■■83062
-
■2■
I
x
■18:058
-
■20。
I
XI
■■7.926
=
■20:735
484 =
930
898。 7
868。 7
.409
886.8
870`■
865。 ■
870.7
860。 5
869。 0
■20。
956
Average
869。
6■
■.ユ
Ttr
Present work
c■ u三
￨`￨'
ts
ュ
■■9.96
and‐ w。 ■
= (1124'C
(11111)
+ 0`0■
■20:26
,
In this series′ the transition was conl in Steges。
b
irom reference 3.
C
Frorn reference 5。
■
[139]
●
●
4-5. Thermodynamic functions
The thermodynamic functions of HBr and DBr were
ca1cu1ated.Thecontributionoftheheatcapacities
below 2 K was evaluated by a smooth extrapora.tion
The results are given in tables 4-9 and 4-10 for HBr
and DBr, respectiveJ-y. The entropy of liquid HBr and
DBr at the triple points was calculated to be 95.88
and 101.78 J K-l mol-l, which are slightly different
from 96.46 J K-l mol-l by Giauque and wiebe and 100.17
J K-l mol-I by Clusius and wolf' respectively.
鍮 一
ヽ
[140]
■‐‐一 … …■一‐―一 ^∵
… ハ
“ …
:.・
TABLE
¨ ‐T=‐ …■
`
4-9. Thermodynamic functions of,HBr.
●
Ｔ
一Ｋ
so
(r) -so (o)
JK・
mo■・
{no (r) -Ho ( o,
JK-1*mo1 -'l
t
n
-teo (r) -Ho rcl
二
」K■
・ mo■・
So■ id
ゆ
O.653
857
■0
0。
20
5:080
0。
204
3。
736
■3344
■79
3.524
07
6。
30
■0。
70
7。
40
■6。
07
■0。
50
20.96
■2.45
60
25。
52
■4.54
■0。
98
70
29.93
■6.58
■3。
35
80
34。
54・
■8。
83
■5。 7■
9■
44。
05
25。
59
■8.46
■00
48。
02
27.06
20.96
■■0
52。
46
28.841
23.62
■■5
57.02
■20
62。
■30
65◆
■40
■50
002
8e5■ 0
07
24。
95
02
35.62
26。
40
64
36。
32。
35
29629
69。 0■
37.00
32.0■
72。
20
37.62
34◆
58
■60
75。
25
38。 2■
37。
04
■70
78.■ 8
38.8■
39:37
`
[■ 4■
1
t
/r
'
^.い 、
、
Continued.
TABLE 4-9。
●
T
S°
(T)― S°
(0)
i{H°
(T)― H° (0)〕 /T
二{G° (i)― H°
」K・ mo■・
JK・
■80
8■ .02
39。 4■
4■ .6■
■86.5
83。 02
40。 0■
43。 0■
K
.
■86。
5
JK・
mo■・
Liquid
・
95。 88
mo■・
‐
●
`
[■ 421
52.87
43。
(o)}/T
0■
TABLE
4-10. Thermodynamic functions of
DBr.
6
Ｔ
一Ｋ
so
(r) -so (o)
JK-'t-mol-1-
{uo (r) -no ( o)
JK-1.-mo1 -'l
}/r
-teo (r) -Ho rc\ I/r
'l
JK-'t*mo1- -
So■ id
200
■0
0.843
O。
643
0。
20
5.209
3。
7■ 5
■。495
2■ 6
3.674
27
6。
■79
■2.90
8。
763
30
■0。
89
7。
40
■6.44
■0。
50
2■
60
26。
70
3■ 。44
■7.59
■3。
80
36.37
20:O■
■6136
90
42.07
23。 ■9
■8。
.66
60
■5。
28
■■。32
86
88
■00
50。
83
29。 ■5
2■ 。68
■■0
55.63
3■ 。08
24.55
■2■
66。 9■
39.26
27365
■30
70.43
39。
94
30。
49
■40
74。
09
40。
62
33。
48
■50
77。
55
4■ 。25
36`30
■60
80。
84
4■ 。86
38。
■70
84。 0■
42.48
4■
1■
431
98
.53
1,
TABLE 4-■ 0.
Continued。
ひ
r
so
K
(r) -so
」K ・mo■
(0)
'
tno (r) -no (o)
r/T
-{co (r) -no (o',1/t
JK-1-mol_-I
_-1
JK-'r-mol
・
■80
87.■ 5
43。 ■7
43.99
■85。 5
89。 0■
43.72
45.29
Lttquユ d
■85。
5
■0■ 。78
‐
56。 49
[144]
‐1
1
‐
45.29
｀
■ヤ
`｀
REFERENCES tO CHAPTER 4
`
■e silnon′
」.
2。
■489,
A. Zo NaturfoFSChe B.■ 970, 25′
App■ 。 Cryst。
■974,
4′
■38。
Strunk′ W, G。 , Wingate′ Wo H。
■954′ 76′
3: Giauque′
W・
」. Amふ
Chern= Soc.
■025。
F., Wiebe′
R。
0. Ame Cherne Soce
■928′
50′ 2■ 93。
4. Eucken′ A.F Karwat′ E. Zo Physe Chem。
5。
C■ usius′ K.F Wo■
6. MOIntoSh′
55′
D。
f′
G. Zo NaturfOrsche
Bate′ Jo R., Ha■ ford′
■935′ 3′
■923′
」。0。
■8′
495.
′
￨
64.
, Anderson′ Lo C. J.
53■ .
See for examp■ e′ Co■ we■ ■′J・
H・ F Gi■ ■′ Eo
Morrison′ 」。A. Jo Chem, phys。 ■963′
嗜
[■
467.
■906′
｀″
■37。
Chemo Physe
9。
■947′ 2a′
, Stee■ e′ B. D. Z. Physe Chem.
7. Henglein′ Fo Ao Z. Phys.
8。
■924, ■■2′
45]
K。
139′
,
635` ￨
‐
Appendix 4Ao
Measured heat capacities oF HBr.
一Ｋ
Ｔ 一Ｋ
Ｔ
―
cp
JK-'t-noL -1
■03。 9■ 3
45。 73
Samp■ e
エ ー
■05e■ 06
46.50
Ser■ es
エ
■06。
286
47。 40
84。 ■73
46。
70
85.428
50。
92
86。 62■
56:80
■■.232
3。
633
87.733
66。
23
■■。753
3。
99■
88:726
86.40
12.444
4。
639
357.7
■3。 ■53
5.226
■67。 7■
■3.820
5。
840
323
・
{11111}卜
89。
350
90。 ■08
9■ 。357
56
■4。
446
6。
40.92
■5。
048
6.9■ ■
4■ .■ ■
■5.627
7.394
245
4■ 。68
■6e■ 9■
7。
886
96。 5■ 7
42。 ■7
■6.758
8。
356
97.778
42。 7■
■7。
333
8。 8■ 9
027
43。 ■8
■7.9■ 8
9.326
■00.266
43.74
■8。
543
9.785
■0■ 。493
44。
43
■9.208
■0`293
709
45。
07
92。
ヽ
■
Series II
663
93.96■
95。
99。
■02。
40。
い
[■
46]
Appendix
4A. Continued.
●
Ｔ二 Ｋ
Ｔ
一Ｋ
Ser■ es エエエ
■■。792
■2。
●・
■
607
11111111)
251884
078
‐
26。
4.765
680
JKllmo■・
■4。
265
■4.69■
■5。 ■■■
■3.373
5。
433
27.475
■5.526
077
6。
002‐
28.270
■5.9■ 9
■4.724
6。
589
29。
065
■6.3■ 2
■5.329
7.■ 50
29。
868
'■ 6.702
■5.9■ 4
7.622
30。
677
■7:04■
■4。
■6。
485
8。
■28
3■ 。493
■7。 4■ 3
■7。
046
8。
597
32。
320
■7.723
■7。
602
9。
052
33。 ■57
■8。
9.527
34.008
■884■ 3
■8。 ■88
`1〕
4。
099
25。
Cp
873
070
735
■8。
825
■0。
■9。
504
■0.535
35`756
■9。 068
20。 2■ 0
■■。067
36.657
■9。
2■ 。006
■■.62■
37.582
■9.673
2■
.859
22.69■
23。
506
24.307
028
34。
■8。
365
212
38。
532
20。
■2。 770
39。
480
20。 30
■3:3■ ■
40。 403
20.6■
■3。 790
4■
1328
20。 88
■2。
主、
[■
47]
00
Appendix 4A.
Continuod,
い
Ｔ 一Ｋ
Ｔ 一Ｋ
●「
t
-p
iIK-l -mo1 -1
42.257
2■ .■ 5
4。
43。 ■9■
2■ 644
5:007
0`2888
44.■ 29
2■ .72
5。
546
0.4■ 8■
451075
22。
03
6:0■ 6
0.5294
46.027
22。
30
6:494
0。
362
0。
■904
6882
989
22.57
47.96■
22185
48。
943
23。 ■6
6.005
‐
0152■ 5
49。
936
23.44
6.4■ 6
■
0=6587
50.942
23:78
6`93■ ￨
0。
5■ 。960
24。
7.494
1
■:■ 06
8:068 .￨￨
■.43■
8。
6481 .
■:739
9。
269 1‐
2.■ 36
9。
963 11
.2.6■ 5
46。
Ser■ es Vエ
06
SerieO 工V
2.569
060338■
serieg v
3。
229
′4。
044
63■
0。
03652
■■:768
2。
954
0。
05■ 8■
■3.0■ 2
3。
269
0。
07354
0。
■099
.704
(0・
l■
48]
8545
10.783
2。
3。
￨
53■ 04
￨二
`キ
ヽr,ヽ 炒響
・ .・ r
鶴率ヽヽ、後
Appendix 4A.
Continued.
い
Ｔ 一Ｋ
Ｔ 一Ｋ
i CI‐
」Kl・ mo■ ll
Ser■ eS Vエ エ
ウ
‐
Cp
■
■ttll品 ■
5.936
0。
5226
6887
7.499
■。■13
6.552
0。
8。
■38
■。449
7.■ 52
0:9679
81‐
788
■.832
9。
483
2。
■0。
265
2.839
■:722
■■.■ 8■
3.555
1.995
0。 0■ 5■ 9
■2。
208
4.402
2.254
0。
02564
■3。
345
5.42■
2.502
0。
05462
2.7■ 0 ,
0:05842
2:999111
0`05765
280
Ser■ es
Ser■ es V工 II
1
3:856
O.■ ■96
3。
276
0:■ 764
3.859 1
4。
4.694
0。
24■ 8
5:■ 38
0。
3■ 77
5:56■
0。 4■
453111
Serュ es
28
4。
340
4.633
0。 0■
0。
08328
0:■ 349
X工
￨
0.■ 95■
0。
235■
SOries IX
4。
978
5.392
O.2963
0。
Ser■ es XII
3798
5■
う
1■
49]
.066
056
23:72
サ
“
: :Ⅲ ● ｀ :
.。
Ⅲ
l
■
´…… …・ …
………… ・
,`…
Appendix 4A.
ャ
Continuё d.
い
Ｔ 一Ｋ
Ｔ
一Ｋ
●「
り
_Cp
泳
■
m■
■
5■ .6■ 2
23.92
71.520
3■ 。93
52.393
24。 ■7
72。
440
32.54
53.356
24。 5■
73。
348
33。
54。 4■ 6
24.77
74。
244
33.75
25。 ■■
75。 ■28
34.42
55。
457
08
56.480
25。
46
761000
35。 ■6
57。
484
25。
80
76。 86■
35.86
58。
505
26.■ 4
77:7■ ■
36.7■
59。
542
26。
60.563
6■
.602
53
78。
548
37。
58
26.93
79。
374
38。
65
27。
37
80。 ■87
39。 5■
989
40。 681
660
27.76
80。
63.702
28● ■8
8■
64。
728
28.57
82.55■
43。 43
65。
739
29。 0■
83.3■ 2
44。
66.736
29.44
67。 7■ 8
29。
92
68。
689
30。
35
83。 6■ 7
45。
69。
645
30。
97
84。 ■87
47.27
70。
589
4■
3■ 。
747
48。 93
62。
.777
42。
03
99
Series XIII
84。
[150]
50
Ⅲ
出二 ■1 ■
‐
)
￨
′
キ
￨￨￨￨￨・
シ .'1:
. =1
‐
i
l l
‐
11
'1
Appendix 4Ao
●11
`
.
1
1= tti lt` ':u .1
1 , i l_
:￨.,11 11
:
｀' ■
■1 ,lt
.
l
,
‐
1・
Continued.
◆
Ｔ 一Ｋ
Ｔ 一Ｋ
″
85。
297
50。 9■
96。
750
42。
37
85。
835
53.■ 3
97。
800
42。
57
86。
360
55。
56
98。 9■ 7
86。
864
58。
97
■00.438
43。
93
87.35■
62。
88 1
■02。 ■■8
44。
84
87。
829
67。
59
■03:578
45。
60
88。
285
74。
60
■05。 0■ 3
46.52
43.27
88。 7■ 3
84:47
■06。
598
47。
64
89。 ■04
■01.62
■08。
327
48。
96
249。 9
■■0:024
50.54
■■■.686
52。
89。
386
Transition
244.7
89。
734
90。
069
58。 5■
90。 587
40.90
9■ 。■43
40。
85
.697
40。
77
248
.40。
9■
92。
■■3.009
729
.41.。
■3■ 。09
Transュ tion
■■4。
575
■■6。 ■24
59。 68
1
57.38
Transュ tion
98
Ser■ es X工 V
95。
46
88
[■ 5■
1
■■7。
228
352。 3
■■8。
324
45。 02
■20。
036
45。
■6
1
.「 1
.
￨
.
1 1:
｀■ .
Appendix 4A.
Continued.
l●
Series
●
・
Ｔ 一Ｋ
Ｔ 一Ｋ
」K.‐ mol
.
XV
″・
■■0。 346
50。
■■0.987
5■ .42
■
■■■。622
52。 35
1‐
■■2。 25■
53。 ■6
■■2.1875
54.■ 6
375
■33。 4■
65
:JK `mё ユ
=
TFanSition '
■■7.■ 37
1 223.6
■■7=595
1‐ 45:02
■■8.250
11 44。 98
´■
■■3。
.
い
.
Iransition
■14。
040
エエ■工.
80.23
56。
78
207
52。
97
■■51824
53.59
435
55`29
■■6。
1■ 9.557
1 45.29
Ser■ es xVII
■■4.596
■■5。
■18。 905 11 45。 ■0
TFansitiOn′
continuou,I Hea11,g
Series XVIII
Ir-I Transition,
Continuous Heating
Ser■ es
WI
■14.■ 28
49.33
■■4。 764
50:75
It-I Transition,
■■5.392
52.■ 8
Continuous Heating
■■6:00■
53.73
■■6.59■
59。
Series XIX
63
[■ 52]
Appendix 4A.
Continued。
●
Ｔ 一Ｋ ﹂
Ｔ 一Ｋ
Series
92
■4■ .66■
45。
II-Ir Transition,
■44。 ■9■
46。 ■7
Continuous Ileating
■46.7■ 7
46。
■49。 24■
46.65
.762
46.75
「
●
XX
Series XXI
■5■
35
II-I Transition,
■54.265
47。
Continuous Heatilg
■56:765
47.3■
■59。
262
・ 47。
04
53
Ser■ es XX=エ
■6■ 。74■
47.93
■■8。
908
45。 ■4
■64.■ 99
48。 ■5
■20。
364
45。
09
■66。
648
48。
48
■2■ 。956
45。
07
■69。
084
48。
74
682
45。 ■7
■7■ 。5■ 2
49。 ■7
■25。 58■
45。 ■7
■73。
920
49。 5■
■27.752
45.■ 8
■76.330
50.00
■30。
084
45.2■
■78:692
50◆
■32。
402
45。
■23。
■34.703
05
34
Series XxIIエ
45。 4■
■36。
990
45。
■39。
264
45.72
68
■80。
888
■82。 9■ 3
[■
531
50.84
5■ .4■
Appendix
4e. Continued.
Ｔ 一Ｋ
Ｔ 一Ｋ
■84。
758
55`08
Fus■ on′
C6ntinuous Heating
58。 50
■88.3■ 6
●
r
87。
497
63.50
88。
005
69.62
88。
483
78。 ■■
88。
926
9■ 。57
89。 29■
■28.95
Transュ tion
Series XXIV
■84。
89:667
59。 74
933
Fus■ on
89.972
74。 20
495
4■ 。02
.086
40。 84
676
40.89
■88.406
59。
53
90。
308
59。
93
9■
■90。
336。 2
9■ 。
― Samp■ e 工エ ー
Series I
Iエ エーエエ
Ser■ es IIエ
■■0。 400
Transition′
Continuous Heati,g
50。 93
■■■。0■ ■
5■ 。23
■1■ 。6■ 8
52.34
seriё g ェェ
■12。 2■ 8
52。
65
850
53.30
■■2.779
53。
88
86.417
55。 90 .
■■3。 30■
54。
50
86.966
58。 77
85。
Transition
な
[■
541
Appendix 4Ae
Ｔ 一Ｋ
■■3。
●
Contintё de
cP-
-
・
訳 l・ mOrl
645
T
K… f∵
l・ .・
Series V
353。 9
■■3:94■
75。
44
■。835
0。 0■ ■
■■4。 4■ 9
54。
60
■。849
0。 0■ 2■ 0
■■4:940
5■
679
2.002
0。
01489
■■5。 1464
52。
57
2.2■ 0
0。
02099
￨
■■5。
985
53」 75
2。
448
1■ 6。
499
55.79
2。
757
■■6=861
-
Transition
■■7.4■ 6
■■8。
224。 5
048
44。
96
20
0.02880
.
3.■ 22
0。
3.48■
0.09060
3.9■ 6
0。
0632■
■320
44`94
series
Ser■ es
0104■ 87
工V
V工
l.842
1
0。 0■ ■
・
0。 0■
40
`630
49。
35
2.045
■75。 ■0■
49。
48
2.282 1
0.02334
538
50。
27
2。 5■ ■
0。
03■ 29
■7■
■78。
605
■8■ 。634
5■ 。03
2.803
0。
043■ 4
566
62。 2■
3。
■58
0。
06532
3。
522
0。
09309
■84。
Fus■ on
3.880
●
[■
55]
1
1 0.■ 273
Appendix
4A.
ConLinued.
●
K
4。
l .=ト
」K・ 嵐o■・
263
0。 ■726
Series vIエ
●
‐
42
■1824
0。
0■ ■
■。
988
0。
0■ 5」
6
2:202
0102■ 20
2.542
0103232
:
Seriё s vエ エエ
3。
902
4.293
4.652 1
4.969
0。
■274
0。 ■705
0.2276 .
‐
‐
0。 2833■
5。
292
0.3435
5。
637
0。 4228
5.980
0:5208
6.374
0。 6429
6.879
0.8756
7.456
■。■05
‐
￨
.
0
[■
56]
App*endrx
48.
Measured heat_lanacities
of
DBr.
●
Ｔ 一Ｋ
Ｔ
一Ｋ
serュ es エエ
―
●
Samp■ e
エ ー
■.884 1
0.0■ 267
Ser■ es
エ
2:053
0。
0■ 767
2.278
0。
023■
■.887
367
090
0。
0■ 763
2。
542
0。
0345
2。 3■ 0
0。
0256
2。
788
0。
0434
2.595 1
0。
0348
3.038
899
0。
047■
3。
292
0。
076■
3.209
0。
0648
3。
533
0。
0992
3。
492
0。
08■ 8
3.782
0。
■■78
3。
760
0。
■047
4。
045
0。
■50■
4。
027
0。
■308
41295
0。
■8■ 6
4。
282
・
0.■ 654
4。
544
0.2064
4.840
0。
283
4。
814
0.259
5。
■45
0。
336
5.105
0.3■ 0
5.432
0。
388
5.8■ 6
0。
485
■.90■
0。 0■
484
6.257
0。
626
2.■ ■9
0。 0■
950
2.36■
0。
2。
QI
0。 0■
2。
4。
56■
0.0559
0.2■ 28
ser■ es エエエ
[■
57]
0255
f蹴 1■
ギ
.11
サ
・1｀ 一 ‐
一守∵
48.
Appendix
…
…………………
………………
Continued,.
●
一Ｋ
_
・
2.608
0。
0373
9..74■
2.453
2.870
0。
0484
■0。 722
3.■ 87
3.■ 54
0。
0680
■■。735
3.96■
3.428
0。
0838
.
707
3。
ゆ
」K ・ Ino■
Ｔ
Ｔ 一Ｋ
●
Cp
3.984
Ser■ es V
0.■ 094
0。
■4■ 5
5。
82■
0。
464
6`287
0.603
225
6.797
0。
0。
27■
7。
484
■。072
■52
0。
347
8。
329
■.5■ ■
5.525
0。
4■ 9
9.247
0.430
■0。 226
4。
256
0.■ 861
4。
530
0。
4.827
5。
5。
58■
Ser■ es 工V
2し
1 1
783
093
2.797
■■.233
3。
56■
■2。 3■ 9
4。
458
346
5。
263
6。
077
677
O。
420
■3。
6.■ 02
0。
536
■4:23■
6.578
0.697
■5。 ■03
7。 ■
42
0.942
■5。
7.883
■。274
■6.895
8。 4■ 7
786
■。787
■7。 853
9`249
5。
8。
●´
[■
58]
985
‐
6.865
7。
65■
Appendix 4Be
C6ntinued.
Ⅲ
Ｔ
一Ｋ
Ｔ 一Ｋ
Cp
」K ユ
mo■
・
「
■8.886
■0。
008
66。 ■30
3■
20。 02■
■0。
884
67:■ 67
32。
43
68.202
32。
87
69.232
33。
30
Series VI
●
`
.96
49。
947
25`28
70.262
33.97
50。
975
25.83
7■ 。303
34.50
356
35。 ■2
5■ 。992
26。
03
72●
002
26.32
731422
35。
85
54.005
26.75
74.500
36。
49
000
27.09
75.595
37.20
53。
55。
55.985
27。
54
76.703
138。
56.972
27.99
77.8■ 9
138`85
964
28。 3■
78。
927
40。 0■
57。
‐40。
09
96
58.96■
28。
78
80。 02■
59.96■
29。
26
8■ .■ 02
42.■ 2
60.967
29669
82。 ■66
43.27
6■ 。984
30。
08
83.2■ 0
44.53
63。 0■ 0
30。
56
84。
239
45。
89
64。
046
3■ 。00
85.236
47.95
65。
089
3■ 。
35
86。 ■84
49。
■
[■
591
63
AppendiX 4Be
Continued`
も
Ｔ
Ｔ
一Ｋ
一Ｋ
5■ 。
87.863
553
88。
り
62
87.070
78。
357
39.36
53。 7■
79。
456
40。
56e■ 0
80.538
4■ 。45
。608
42.67
82.662
43.77
‐
89。 ■92
58。
89。 8■ 8
6■
90.43■
65。 ■■
831702
: 45。 ■6
69.■ 4
84.720
46.85
9■ .6■ 3
761■ 9‐
85。 70■
48.55
92。 ■75
84.42
86.636
50。 4■
95
87。 5■ 3
￨152.24
55.■ 7
9■
.029
92。
706
67
40
.66
98。
8■
‐
93。 ■86
■3■ 。■2
88。
294
93.5■ 6
433:0
88。
974
TranSition
94。 ■■7
■97。 0
94。 45■
57。
95。
089
Ser■ es
54
46。 73
35
896542
160。 ■6
90。
098
1 63=40
90。
702
1 67105
.293
7■ 。73
91.864
1 78.92
92。 4■ ■
‐ 89:26
9■
VII
157。
76.■ 39
37.45
92.923
■08.3■
77.246
38。
44
93.354
■82.74
[■ 601
Appendix 49. Continued.
●
」K・
mo■・
■08.707
793
■■0。
404.6
■08。
58
94。
777
47:65
95。
609
46。
69
series vIII
075
52◆ 6■
53。
69
■■■。440
54.78
803
55.83
■■2。
′
●
■■4.■ 62
57。
46
■■5.504
59。
32
■■6●
825
6■ .■ 4
Transition′
■■8。 ■23
66。
continuous Heating
■■9:050
324。 6
Iエ エ"エ エ
74
Transュ tion
94:763
47.84
95。 79■
46.72
■20。
96。
887
46.95
■2■ 。44■
49。
98。
054
47。 4■
■22.635
49。 ■5
99。
297
47。
65
■00。
596
48。
08
' lL口
111111)
JK-1*mol -'l
Transュ tion
94。 ■43
●
Cp
一Ｋ
一Ｋ
93。
Ｔ
Ｔ
Cp
432
80.39
89
series lx
■0■ 。923
48。 6■
エエI― II
280
49.2■
Continuous Heati,g
■03。
TFansition′
■04.645
50。
03
95.062
46。 93
997
50。
99
96。
280
47。 02
5■ 。79
97。
439
47.04
■05。
■07.348
心
116■ ]
Appendix
48.
Continued..
●
Ｔ
Ｔ
99。
●・
976
一Ｋ
一Ｋ
98.678
47。
36
48。
28
■02。 62■
48。
80
962
49。
52
■05.302
50。
44
■06。
654
092
49e■ ■
47.77
■0■ 。289
■03。
■22。
Series
X
II-I Transition,
い
Continuous Heating
5■ .27
Series xI
■08。 0■ 4
52。
05
II― 工
373
53。
08
Continuou, Heating
■09。
■■0。 7■ 9
Trans■ tion′
53。 97
■2■ 。482
49。 00
064
55。
22
■22.969
48。 92
■■3。 4■ 5
56◆
99
■24.573
48。 90 1
■■4.76■
58。
39
■26.29■
48。 98
■■2。
■■6。
094
59.68
■28.■ ■9
49。
■■7。
408
6■ 。90
■30.058
49。 ■8
■■8。
446
72◆
82
■3■ 。983
49。 ■5
■■9。
035
26■ .5
■33.898
49。
40
■35。
799
49。
50
■37。
709
49。
62
Transit,ion
120。 ■53
120.896
2■ 6.6
■39.696
49。 48
[■
62]
04
49.73
Appendix 4B.
Continued.
Ｔ
e724
24。
49。 9■
492
7■
」K‐
・ mo■
■4.04
■43.734
50。
00
25.538
■45.823
50。
28
26。
594
■5.27
50.36
27。
626
■5。
84
28。
619
■6。
39
29。
579
■6.90
■47。
●
一Ｋ
Ｔ 一Ｋ
■4■
Cp
985
■50:■ 34
50。
50 ・
も
ser■ es Xエ エ
■4。
66
30。 5■ ■
■7。 37
■■.547
3.836
3■ 。439
■7:82
■2.506
4.642
32。
385
■8。 27
529
5。
523
33。
372
■8.74
■4.578
6。
504
34。
432
■9.22
586
7。
343
35:542
■6.559
8。
■95
36。
633
20.■ 7
■7。
492
8。
979
37.690
20.53
■8。
459
9.768
38。 7■ 8
2■
■9。
475
■0。 529
39.73■
2■ 。39
20。
565
■■。34■
40`738
2■ .8■
08
4■ 。743
22.22
■2.72
42.74■
22。
53
749
22。
97
■3。
■5。
2■
.605
22。
532
23:48■
■2。
■3。
37
43。
[■
63]
■9。
68
103
みppendix
4B.
cOntinued.
●
Ｔ
Ｔ
一Ｋ
一Ｋ
-p
iIK-1*mol,-1-
779
23.35
45.832
23.76
46。 9■ ■
24。 2■
Series XIV
24.6■
Fusion,
44。
48。
0‐
■8
49:■ 90
25。
■87.638
02
62.60
Continuous Heating
tl
Series
■52.399
‐ Samp■ e
XIエ エ
50。
80
II
―
‐
series I
004
5■ 。■0
48。 438‐
■57.6■ 9
5■ :■ 5
50。 ■76
■60.266
5■
.60
■62.920
5■
`93
■65:553
52.26
■68。 ■89
52。
67
57:272
826
53。
63
58.9■ 3 11 28■ 75
■55。
■70。
25。
34‐
039 1 .
26。
05
53:839 1 1
26。
73
27。
40
28。
08
52。
55。 58■ ￨￨‐
54`09
60.5■ 0
■76.■ 03
55。 ■0
62.067
736
56.62
63。
.324
63.85
■8■
Fus■ on
[■
64]
24:66
1
■733464
■78。
‐
738
_
1
‐
29:42
30。
09
30。 8■
…
みppё ndiX 4B,
cOntinued.
0
Ｔ 一Ｋ
Ｔ ¨Ｋ
Ser■ es II
JK・ mol l
36892
0。
O。 0■ ■
97
4.2■ 7
0:■ 620
10。 0■ 796
4.569
0:2■ 56
0268
4.958
0.287■
2`819
0:043■ .
5:378
0。
3.■ 48
0。
06■ 0
3.42■
0。
0825
■.880
こ
Cp
2。
■22
2。
428
3.7■ 3
0。
‐
Sё
ries
0e■ ■■8
■。879
■208
3822
工V
O。 0■
320
4。
056
0.■ 534
2。
4。
40■
0:■ 9■ 8
2,4■ 5
0.0295
4。
833
0。
2787
2.7■ 7
0:0390
■29
3。 0■
Ser■ es エエエ
4
'0。 0■ 903
1
31327
.0。
0548
10107291
■。888
0。 0■
274
3.65■
2.■ 26
0。 0■
885
3.983
10:■ 3■ 8
2:40■
0。
0276
343
01■ 774
2。
707
0。
0400
3。
004
0。
0529
3.297
3。
590
4。
Ser■ es
0.0727
0。
0949
65]
V
4.7■ 0
O.2274
86
10。 3■ 74
5。 ■
[ユ
0.■ 000
￨
‐
'― ―
Appendix
十 ^■―
・今‐ ‐
―
・― 午 ■
‐r― ―
',11=―
・
4。
45■
48. Continued.
a
Ｔ
Ｔ
一Ｋ
一Ｋ
5。
708
0。
4307
12。
6。
270
0。
5978
■3.278
6。
870
0。 8■ 8■
306
5`327
Ser■ es Vエ エエ
‐
Ser■ es V工
●
4。
870
5.356
0。
2528
8。
■25
■。40■ 0
8。
844
■.85■ 8
9.546
0.3488
2。
308
880
0。
4906
■0。
269
2.825
6.436
0。
6629
■■。043
3.440
7.032
0。
8947
■■。88■ 1
4e■ 29
7.725
1。
2■ 29
12。 8■ 2
4.934
■3。 8■ 6 1
5。
5。
745
Ser■ es Vエ エ
Ser■ es
7。
4■ 7
■60609
8。
048
■.3795
■57:262
8。
664
■.73■ 2
96297
工X
5■
.25
■59。 723
5■
.47
2e■ 48
■62。 ■66
5■ 。79
957
2。 6■ 4
■64。 6■ 3
52。 3■
■0.655
3.■ 47
■67.085
52.60
■■。428
3。
752
■69.577
52198
9。
t
[■
66]
■
出 “∴ 4・ ‐1.・ I
Appendix 48. Continued.
ヽ
い
l
・
●
i
■72。
087
53.67
■74。
613
54.32
■77。 ■58
56.34
■79,737
57.■ 0
■823■ 69
64。 00
い
Fusion
■88。 ■79
62.15
■
い
[■
67]
●
CHAPTER 5
Therlnodynamic Properties of
●
HI and DI
り
(
[■
68]
●
●
●
5-1. Heat capacity
The measured heat capacity values are chronologically
presented as Cn in appendices 5A and B for HI and DI,
respectively. Curvature corrections were not applied.
The smooLhed values at rounded temperatures are given
in table 5-1. Above l-50 K, corections arising from
vaporization of HI or DI were significant. Relevant
quantiti-es for such corrections were evaluated as
follows. The d.ensity of sol-id HI in phase I was
obtained by interpolation of the X-ray data at 125 K(1)
and at triple poirrt!2) The liquid density vras taken
from Mclntosh and steetei3) Densities of DI were
taken to be id.entical to those of HI. The heat
capacity in the gaseous phase is (7/2lR in the
temperature range where the values was required.
The results for HI and DI are plotted in figures
5-I and. 5-2, respectively. The measured heat capacities
are compared with earlier resul.ts in figures 5-3 and 5-4
for HI and DI, respectively, in terms of the differences
from a smooth curve corresponding to the val-ues given
in table 5-1. The scatter of our measured points is
13 per cent at the lowest temperatures, decreasing to
+0.5 per cent at L0 K and to 10.1 per cent above 20 K.
It increased, howeverr up to +0.2 and +I per cent at
higher temperatures and near the transitions, respectively.
`
'1■
691
TABLE 5-■
。
The heat capacity of solid. HI and. DI
at rounded values of temperatures.
`
Ｔ
一Ｋ
H工
●
D工
0282
0。
0267
0。
094
2
0。
3
0.■ 00
4
0。
5
0.559
0.545
6
■。023
0.996
8
2。
447
2.4■ 4
■0
4。
358
4。
■2
6。
496
6.50■ ‐
■5
9。
649
9●
20
■3。
97
■4e■ 3
25
■7。
08
■7e37
30
■9.40
■9。 9■
35
2■ 。38
22.24
40
23。
30
24.68
45
25.44
26e77
50
27。
55
3■ 。28
32.33
60
36。 ■■
36。
/
0.25■ ￨
26■
365
i
98
29。
[170]
74■
35
03
‐
TABLE 5-■ .
Continued.
Ｔ
一Ｋ
InOIア l
DI
HI
65
44.83
70
40。
95
48。
68
75
36。
34
80
37。
26
43。
85
85
38。
63
43。
92
90
40.24
45.■ 6
95
4■ 。89
46。
75
■00
43。
78
48.60
■■0
48。
74
53。
04
■20
56.65
59。
96
■30
44。
■40
45.03
48。
■50
45。 4■
48.25
■60
45。
84
48。 2■
■70
46。
32
48。
39
■80
46:86
48。
67
■90
47.52
49。
30
200
48.2■
50.09
2■ 0
49。
23
50`69
217
50。
47
5■ 。21
48.66
94
[■
71]
37
へ
゛
Ｅ
Ｔち ＴＹ つ＼
０ ５
０ ０
６ ４
゛
Ｔち Ｅ ＴＹ つ ＼
［ＰЧＮ﹄
of HI.
Heat capacitY
FIGURE 5-■ .
lo
5
●﹁
●
費
戸/K
T/K
●
今
/K
戸
Ｅ
戸 /K
Ｃ
■ ｏＥ Ｔｙつ ＼ 。
Ｏ ．５
゛
ＴＹ つ ＼
０ ０
６ ４
Ｔち
［Ｐ呵ω］
Heat capacity of DI.
FIGURE 5-2.
1o
5
0
●
●
●
15
10
︻ＨЧ卜］
①Ｑ ＼︵ИＮ
⊂００ ﹂
一
5
0
十 十 十 T十 十
-5
― 10
― 15
0
50
100
戸 /K
150
200
0′ present
A compar■ son of heat Capac■ ty results for solid HI・
4)▲
u■ ts, +′ Giauquё and Wiebe∫
rさ ζ
′Eucken and Karwat15)
Δ/P'r C'五 t = [9p(° bSO)IC`lSm° °th)]挙 10, / [C`〈 S口 。9th)]' Wlere c3(SmO° th)iS
｀
given in tab■ ё 5-■ 。
FiCURE 5-3。
C
ヽ
15
10
●
θ
●
0
●
・
t
o o -o
OV
０●
［Ｐ劇い］
Ｃ００ ﹂
ＯＱ ＼、ИＮ
一
5
・・ もi「
●
。。
●
。
00
°
●
●
.●
●
-5
●
―10
=15
0
50
100
150
200
戸 /K
FIGURE 5-4. A comparison of heat capacity results for solid DI. o, present
results; o, Clusius ana wotfi6)
A/per cent = [Cn(obs.)-"n(smooth)7 x LOO / [Cn(smooth)], where Cn(smooth) is
given in table 5-1.
for HI are in good
agreement with the present resul-ts within the combined
limits of error. Some of their points near 175 K
showed a broad hrsnp probably due to distilLation heat
effects. Eucken and Karwat ' = t'S) and CJ-usius and
wolf,s(6) resurts are strongry scattered. and deviate
from ours as reported for other hydrogen halid'es'
A comparison in the lower temperature region is made
by use of equivalent Debye temperature OO, whose
temperature dependence for 3N degrees of freedom is
shown in figures 5-5 and 5-6 for HI and DI, respectively.
The Debye temperature curves for HI and DI agreed onLy
between L0 and 15 K: The latter is consistently higher
Giauque and Wiebe's resuLts
ウ
づ
beLow L0 K and decLines more rapid.Ly above 15 K'
ξ
1■
76]
■●
0
●
■
Ｘヽ ご
Ｈｑ﹃］
［
70
T/K
The Debye characteristic temperature of HI derived from
the measured heat capacities, assuming 3N degrees of freedom. o, present
results i *, Giauque and Wieb"J )
FIGURE
5-5.
●
・
・
′
70
′
● ●
︻一ヾ∞﹄
Ｘ＼ 口
０
●
●
●
●
戸/K
FIGURE
5-6. The Debye characteristic temperature of DI derived
the measured heat capacities, assuming
results; o, Clusius anA wotfi6)
3N degrees
of freedom.
froIII
。′ present
5-2. Vapor pressure
of the soLid and liquid HI
and DI are listed in tables 5-2 and 5-3, respectively.
The resuLts f:or soLids were plotted as 1-og P against
-l
in figure 5-'7 . Measurements by other worlcers are
T-r
also incLuded for the sake of comparison. Our results
for both solids and Mclntosh and SteeLe's result"(7)
for HI indicate that the sLope decreases at lower
(8)
temperatures. fn contrast, Henglein' s t""ol-t"
for HI, which consist onl-y of three points, are
approxi-rnately colinear in this pLot. One of
possibilities that might give such an effect would be
existence of permanent gas, which is supposed. to be
hydrogen as one of d.ecomposing products. Estimated.
amounts of permanent gas are 900 and 410 Pa at 180 K
for HI and DI, resPectively. However. no corrections
for the pressure values obtained were made. There were
no indications of d.ecomposition in the temperature drift
of heat capacity determinations nor in the purity
determination at the tripLe point which was conducted
after all the vapor pressure measurements had been
Measured vapor pressures
◆
concLuded.
I■
79]
TABLE
5-2. Vapor pressures of HI.
●
kPa
kPa
Liquid
So■ id
●
■803905
4。
■80
223.505
53。 ■52
■83。 5■ 5
4。
822
224。 ■88
55。 ■45
■86。
097
5。
6■ 5
■88。
670
6。
559
.220
7。
688
■9■
■93。 82■
9.05■
665
■96。
399
■0。
■98。
972
■2.556
20■ 。566
■4.796
459
204。
205
■7。
206。
825
20。 53■
209。
432
24.076
2■ 2.009
28.■ 26
565
32。
722
217.085
37。
892
2■ 4。
2■ 7。
746
39.5■ ■
2■ 9.86■
44。
370
220.2■ 8
45。
384
[■ 80]
TABLE
5-3. Vapor pressures of Df.
●
kPa
kPa
Liquid
So■ id
■78。
■8■
969
3836
■84。 6■ 5
769
5■ 。475
4.233
223。
960
54。
■68
■90。 ■29
6。
300
■92。
864
7。
665
■95。
578
9。
288
■98。
278
■■.2■ 8
200。
954
■3。
203。
672
■6.■ 85
206。
366
■9。
479
228
209.039
22`776
2■ ■。757
27.039
4.452
3■
:932
379
38.329
2■ 9.974
45.28■
269
45.380
2■ 7。
220。
220。 94■
5■ 。278
222。
5。
2■
222.705
472
3。
382
■87。
●
2.838
47。
038
1■ 8■」
572
●
ヽ
ヽ
0
4,5
△
も
3
．
０
．
▽
￨
名
０
ｐ．
．
4.O
０
▼
▲●
ｏ征＼Ｌ ︶０２
︵
●
●
O
●
°
●
o
OO
'\O
a
3.5
4.5
5。
0
5。 5
losK/T
5-7. Vapor pressure of solid. HI and DI.
Hr: o, present results; A, Mcrntosh and steere;(7)
v, ttengt"in.(8) Dr: ., present results.
FIGURE
I
182I
●
●
5-3. Enthalpy of fusion
The resuLts of fusion experiments are given in table 5-4.
to compute the
A correction for the /Cpd.T was
.applied
enthal-py of fusion AH, from cumulative enthalpy
H(T^)-H(T,
). Measurements Uy otfr"t workers are aLso
zt
included for the sake of comparison. The mean values
of the enthalpy of fusion of HI and DI obtained were
2855.3 and 284L.2,1 mol-l, respectively.
The triple points of Pure HI and DI, (222.497 + 0.005)
and (22L.511 + 0.005) K respectiveLy, were estimated
from a plot of the equiJ-ibrium temperature against
the reciprocal of the fraction meLted, (see tabLe 5-5).
￨●
[■
83]
TABLE
5-4. The enthalpy of fusion of HI and DI.
２
Ｔ
Ｔ
●
Series
T.
no.
K
H(T2) H(T■ )
Jmo■
・
￨
△
Hf
」mo■
■
HI
219.861
220.2L8
一 一
xxr
xxrra
505
305■ 。0
2856。 0
224e■ 88
3072.4
2854.6
Average
2855。 3
223。
`
Giauque and l0iebe (r929) b
287■ :5+2.■
Eucken and Karwat (Ls24rc
3038。
D工
220.269
zLg.974
一 ¨
)$rrr
xrxa
222。
769
2999。 8
2842.5
222。
705
30■ ■。6
2839。 9
Average
284■ :2
Clusius and Wolf (1947)d
1184]
2863。 ■
TABLE 5-4.
a
b
c
d'
Continued:
rn this series, the fusion was done in stages'
From reference 4.
From reference 5.
From reference 6.
●
1185]
‐
・
TABLE 5-5.
…
螂帯
―
い●
4‐
4ヽ 帖
The tr■
―
.‐
漱 .゛ 舛トヤ‐
黎 ヽ｀ ■ ■●■ 、■■
■■,it中 ‐
●‐‐
"¨ ■
"t● Ⅲ ・
`,■
1
■中 ■ Ⅲ 組 中 ■ 中 綺 囃 関 線 轟 轟 蜘 爆 轟 mぃ 最 醸
ple point oF HI and DI.
Fraction
melted
kPa
K
HI
0。
222.359
250
0.427
222。
400
50。 5■
605
222。 4■ 9/
50。
0。
746
222.433
50.7■
(■
222。
.000)
444
50。
222。 449+0。
59
74
002
497+06005
Tf (pure Hr)
222。
Giauque and Wiebe (]-g2gra
222。 3■ +O。
Eucken and Karwat (Lgzlrb
220e
et aI.
46
0。
0.890
Bates
50。
05
50.5
(1935)c
MiraveLles and MoLes (1925)d
●
1186]
52。
44
"織
轟 ■ ,Ⅲ I
TABLE 5-5。
Continued.
骨
Fraction
T
me■ ted
kPa
K
′
DI
●
`
0。
237
22■ .472
0。
498
22■ .488
48.6■
0。
676
22■ 。494
49。 ■0
0.854
22■
49。
0.945
22■ 。508
(■
。
000)
Tf (pure DI)
.50■
48。 3■
04
49.■ 0
221.,O■ 主00002
221.511+0-005
clusius and woLf (1947)e 22L.23
a
b
c
d
e
1
From reference 4.
From reference 5.
reference 9.
From reference 10.
From reference 6 "
From
●
[187]
48.O
■
t
5-4. Transition in solids
The thermal behavior of two phase transitions of both
solids can be visuaLized through enthalpy change in
the transition region. Figure 5-8 refers to the
transition between phase III and II and figure 5-9 to
that between phase II and I. The d,ifferent series of
results $rere normal-ized. on the high temperature side of
t,ransitions. The transition temperatures vtere then
determined from the point at which the rate of change
of enthalpy with temperature is maximum.
No isothermal heat absorption was detected at the
lower transition of HI and DI. Furthermore, the time
to reach equiLibrium after heating was off was about
10 min, which is approximateLy normal- equiLibration
tirne in this temperature region. These facts sugigest
that III-II transition of HI and DI is of the second
or higher ord.er. At the upper transition of HI and
Dr, a consid.erabLy Longer equilibration time was
required; thus the cooLing drift at L00 min after
heating was about -0.002 r min-l, which is Large
compared with that at the III-I transition of HCL
and DCl, II-I' transition of IIBr, of II-I transition
of DBr. Therefore, the II-I transition of HI and. of
DI, through it appears diffuse in figures 5-1 and 5-2,.
is of the first ord.er with a Latent heat at the
●
1■
88]
t
●
合
2.2
20
８ ６
・
・
［Ｐ∞０い
Ｅっ
ｘ＼ ︷
〇ざミよＬｒミ ︸
︵
■ｏ
/
/
ノ
/
14
66
68
70
72
74
76
78
80
ア/K
FIGURE 5-8。
Entha■ py change in the regiOn phase III
→
phase II of Htt and DI.
The different series of measurements are noニ ュa■ ized on the high temperature
side of transitionse H工 8 0′ (XIV), △′ (XV)F‐ ▽′ ・(XVI). DI: ●′ (I), ▲′ (III).
:ι
t
も
cID
打１
／︲
▲
︱卜
ゴ
´
一
″
才
A/・
5.5
“
―
▲
´
一
０ ５
５ ４
○ざミ ︲︵
Ｋざミ ︺
Ｔ５Ｅ つｘ＼ ︷︵
［Ｈり０］
410
122
124
126
128
130
万 /K
FIGURE 5-9。 Entha■ py change in the reg■ on phase II → phase tt of HI and DI.
The differё nt series of measurements are noこ llla■ ized on the high temperature
Side oF transitions.
H18 0′
(=■ ), △′
(III).
D18.
● ′￨(V),
▲′
(VI),
transition point. The enthalpy change at the
transitions measured are shown'in tables 5-6 and 5-7
for III-II and II-I transitions, respectiveLy.
As for the "transitions" at.I0 and 25 K, which were
ind.icated by spectral- studies r rlo anomalies in heat
capacity were observed, as shown in figures 5-1 and'/ox
`
5-5;
●
゛
1■ 9■ ]
5-6. The enthalpy of III-II transition of HI
and DI including the "normal'! part of heat capacity.
TABLE
゛
TSeries
TI
'-2
no.KKJmolJmol
H(To)-II(T1
-'.-z',-',-L' )
H(7f)-H(68)
HI
o
xrva
xva
xvra
)ffrr
)ffrrr
082
68.108
68.390
67.gg2
65.831
68.
71.030
7L-. 040
70.954
70.678
70.985
26L.8
260.1 . '
239.5
252.L
377 .6
- 265.L
264.8
264.8
264.8
265.2
Averege
26409±003
Ttt
Present work
70。 23+0。
(1929)bEucken and Karwat (Lgzlrc
70.1
Giauque and wiebe
[■
92]
´
72.'
02
TABLE 5-6。
Continued。
Saries
Tl
T2
H(T2) H(T.)
no.
K
K
」mO■ 7・
Jmo■
H(78)― H(75)
・
JmO■
DI
●
ra
rr
rrr"
)(v
75.205 25.063 75.L34 74.6g7
7g.206
77.956
79.673
78.249
350.5
302.5
345.9
329.0
3Lg.2
318.9
3L9.5'
3L9.7
Averagё
3■ 9。
3± 0.4
Ttr
Present work
c■ isius
77:48+0。 02
and Woi= (■ 947)d
a rn this series, the transition
b From reference 4.
c From reference 5.
d From reference 6.
彎
[193]
77.3
was done
in stages.
TABLE 5-7.
DI inC■ uding
the
Ｔ
Ｔ
．
Series
ttnormaL'!
T2
740
IIA
■23。
IIIA
■24.■ 36
xrx
■23。 ■62
xx
■22。
575
H(■ 27)― H(■ 24)
H(T2) H(T.)′
K
no.
う
transition of HI and
part of heat capacity.
The enthalpy of II-I
Jmo■・
」mo■・
959。 ■
945.0
■27.303
954。 0
948e7
■26.993
■000.6
947。 3
858
■026。 8
946`4
Average
946。 9+■ .9
■26。
■26。
957
Ttr
Present work
■25:60+0。 0■
Giauque and Wiebe (Le2e) b
■25:6
Eucken and Karwat
iJszlrc
t
[■
94]
■24。
1
q;'=*a
.\,fu
-i,q .\
lR!
i
TABLE
Series
n。
5-7. Continued.
. T
rv
vo
vra
)(Vr
T.
T2
T‐
L26.773
L26.892
L27.540
L27.236
H(T2) =(T■
Jm。
) H(■ 30)― H(■ 27)
Jmo■
■
'・
DI:
L29.43L L027.5
129.903 1041.5
129.838 gg2.O
L29.433 996.6
・
1039.5
1038.5
1038.7
1040.8
■
Average
■o39。 4+■ 。4
Ttr
work
CLusius and wolf (Lg47')d'
Present
a rn this series, the transition
b From reference 4.
c From reference 5.
d From reference 6.
`
[■
95]
L23.24+0.01
L28.28
Iilas done
in stages.
5-5.
Thermodynamic functions
ち
The thermodynamic functions
む
and WoIf
of HI and DI \^/ere calculated
by using a smooth extrapolation for the contribution
of the heat capacities beLow 2 K. The results are
given in tables 5-8 and 5-9 for HI and DI, respectiveJ-yThe entropy of liquid HI and DI at the tripJ-e points
was calculated to be LLL.Sl- and 1l-8.89 J K-l mol-l,
which are slightly different from LL2.7g J t<-1 moL-l
by Giauque and Wiebe and, !L7.5L J r-1 moL-t O" Clusius
,
respectiveS-Y.
`
[■
96]
TABLE
5-8. Thermodynamic functions of HI.
争
Ｔ
一Ｋ
so
(r) -so (o)
JK-1*mol--'l-
{so (r) -Ho
(o
」K ・ Ino■
I
・
t
/r
-{eo (r) -Ho rc) t /r
.-'t
JK *mol -'l
So■ id
●
■0
■。528
20
7。
70■
■.■ 54
0。
374
3
2。
388
■88
5。
307
8。
387
5。 3■
30
■4.50
9。
40
20.62
■2。
23
50
26.29
■4。
89
60
32。 0■
■7166
■4。
35
70
4■
.80
23。 8■
■7。
99
80
45。
09
20。
57
90
50.2■
26.60
23.6■
r
●
′
66
25。
■■.40
■00
54。
62
28。 ■3
26.49
■■0
59。
01
29。
77
29.25
■20
63.54
3■ 。63
31。 9■
■30
74.08
39。
36
34。
■40
77。 4■
39。
75
37:66
■50
80.53
40。
12
40。 4■
■60
83。
47
40.46
43.0■
■70
86。
26
40。
■80
88。
92
4■ 。■■
79
1197]
45。
72
47
47.8■
TABLE
5-8. Continued.
ゆ
r
so(r)-so(o) {no(r)-Ho rc')}/T -{eo(T)-Ho rc')}/r
」K・ mo■
K
l
JK ・ mo■・
I
JK・
mo■・
04
■9o
9■ .47
4■ 。43
50。
200
93。 92
4■ 。75
52。 ■7
2■ 0
96.30
42。 08
54◆
22
98.68
42.03
56。
65
222。
5
Liquid
222.5
■■■。5■
54。 86
1198]
56165
TABLE
5-9. Thermodynamic functions of DI.
●
Ｔ 一Ｋ
so (r) -so (o)
JK-l -mol-t-
{no (r) -no (o)
JK=・ mo■
},/r
―■
-{eo (r) -Ho rc) } /T
JK-1-mol -'l
So■ id
■0
■。508
20
7。
722
■。■47
0●
36■
345
2.377
9。 3■ 2
5:325
5。
30
■4.64
40
2■
:00
■2.54
50
26.96
■5.40
■■。57
60
32。
86
■8.24
■4.62
70
39。
22
2■ 。55
■7。
67
80
48。
35
27。
48
20。
87
90
53.54
29。
32
24.22
■00
58647
3■ 。07
27.40
■10
63。
30
32`86
30。
■20
68.■ 8
■30
79。
■40
8。
458
44
80
33`38
94
43.59
36.35
83。
53
43。
94
39。
59
150
86。
86
44。
23
42。
63
■60
89。
97
44.48
45。
49
■70
92.90
44。
70
48。
20
■80
95。
67
44。
92
50。
75
34。
●
[199]
・
ヽ ´ 、
デ _Ⅲ
,`
Ⅲ
■
′
‐ 1・
' ￨
TABLE 5-9.
Continued.
●
r
so(r)-so(o) {no(r)-noto) }/r -{eo(r)-Ho (0,}/T
; ".-E- ffiF
■90
98。 32
45.■ 3
53e■ 9
200
■00。
87
45。 36
55。 5■
2■ 0
■03。
33
45。 60
57。
22■ 。5
■06.06
45.88
73
60.■ 8
Liquid
22■ 。5
■■8。
89
58。
7■
●
[2001
60。 ■8
REFERENCES to CHAPTER 5
●
■.
Ruhemann′ B., Silnon′ Fo Z. Phys. Chem.
■93■ , B■ 5′
406。
｀
Am. SOC。
■933′
Mclntosh, D。 , Steele′ B. D. Z. Physo Cheme
■906′
2. Smyth′ C. P.′ Hitchcock′ C= S.
55′
3。
55′
4。
」.
■835.
‐
■45。
Ciauque′ W. F., Wiebe′ R.
」.
Am. Chemo Soc。
■929′
5■ ′ ■44■ 。
5。
Eucken′ A.F Karwat′ Eo Z. Ph,se Chem。
■924′ 1112′
￨ .
467。
6. C■usius′ K., Wo■ f′ G. Z, Naturforsch。
7。
Mclntosh′ DoF Stee■ e′ B. 0. Z. Phys. CheFIt.
55′
■906′
■37。
8. Heng■ ein′ Fo A. Z◆ Phys。
9。
■947′ 2a′
■923′
■8′ 64。
Batё S′ 」. R., Ha■ fё rd′ o. C.: Anderson′ L` c.
」. chem. Phys。 1935′ 3′ 4■ 5。
■Oc Mirave■ ■es′ R.F MO■ es′
5■ 8。
[20■ ]
Eo Anne Espane
■925, 23′
495.
_o暁aも
、‐
` 11
‐
｀
Appendix 5A:
Measured heat capacities of HI.
Ｔ
Ｔ
I
5■ 。57
■■5。 3■ 7
52。
38
862
42.08
■■6。 26■
53。
07
96。 96■
42.60
■■7。 ■98
53。
92
050
42.93
95。
98。
■
一Ｋ
一Ｋ
Ser■ es
■■4.364
99.■ 30
43。
Ser■ es II
53
■00.202
43.85
■0■ 。266
44。
■■3。 ■27
25
,
50。 ■5
097
1 50.87
■■5.060
5■ 。76
52:25
■14。
■02。
320
4438■
■03。
366
45。
34
■16.0■ 4 1
■04.403
45。
74
■■6。
959
■05.435
46.29
■■7。
895
■06。
460
46。 8■
■■8.823
■07。
476
47.33
■■9。
740: : 56.45
■08。
484
47。
73
■20。
647
■09。
484
48。
48
■2■
■■0。
476
49。
02
■22。
■■■。46■
53。
■
42
54。 ■■
・ 55。
‐ 57。
29
49
.545
58.67
430
60.57
49.48
■23.304
6■ 。62
■■2。
438
50。
40
■24。 ■67
64。
06
■■3。
404
50。
83
■25。 0■ 4
66。
06
ウ
[202]
Appendix
5A. Continued.
●
Ｔ
Ｔ
一Ｋ
一Ｋ
Transition
■25。
933
■26。 ■74
●「
◆
■2も
:634
■27。
442
■28。 4■ 5
488.46
360。
07
■07.95
、■■9。
275
■20。 ■82
」K・ mo■・
■27。
789
45。 ■0
■28。
759
45。 ■3
■29:727
44。
95
750
44。
94
■30。
99
■3■ 。8■ 2
44.90
44.98
■33.063
44。
■34.503
44.90
■36。 ■30
44.95
■37.942
44。
96
844
45。
03
45。
Ser■ es III
■■8。 08■
Cp
54.86
56。
05
■39。
57.■ 6
■4■
.740
88
45。 ■■
.079
58。
43
■43.629
451■ 5
■2■ 。966
59。
63
■45。 5■ 2
45。
■2■
■22。
843
6■ 。26
■23.707
62。
■24.558
64.63
■25`337
90。
■47。
98
■49。 26■
99
Ser■ es
Transition
■26。 ■40
■26。
849
52
ロ
[203]
45.3■
45。
38
IV
705
5。
1■ 。
078
5.508
■■。6■ 9
6。
10。
■56.■ 6
53。
389
23
070
077
^F´ ￨=
Appendix
5A. Continued.
●
JK-1*moL-14
■2.269
6.765
■2.962
7。
■3。
682
■4。
cp
一Ｋ
一Ｋ
●
Ｔ
Ｔ
●′
"p
JK-1-mol -1
764
■8.424
53■
28.596
■8679■
8。
295
29。
435
■9e■ 53
426
9。
068
30。
283
■9.53■
■5.■ 59
9。
8■ 6
Ser■ es
V
27。
870
■0.5■ 9
■6.570
■■。■5■
■0。 78■
■7。
264
■■。794
■■.260
■7。
958
■2。
385
■■.894
6。
367
■8ら
656
■2.927
■2.6■ ■
7。
■54
■9.362
■3.493
13.322
7。
907
654
■5。
￨
:
5e■ 70
5.697
20。
080
■4。
025
■4.066
8。
20。
898
■4.60■
■4.8■ 5
96470
.800
■5。 ■98
■5。
532 1
■0.■ 78
2■
22。
684
■5。
756
■6。
234
■0。 8■ 4
23。
555
■6。
274
■66928
■■.505
24.4■ 7
■6。
736
■7.6■ 8
■2。
276
■7。
225
■8。 3■ 0
■2.668
25。
26。 ■■5
26。
937
075
■7。 65■
■9。
009
■3。
227
030
■9。
730
■3。
779
■8。
[204]
0.ナ ‐
‐
Appendix 5A. Continued.
●
Ｔ
Ｔ
一Ｋ
一Ｋ
201549
■4。
343
30.747
2■ 。437
■4。
959
3■
22。
323
■5.54■
Cp
」K ・ mo■
■9.695
.897
33。
20。 ■9
056
20。
60
■6。
066
34:228
2■ 。09
072
■6。
570
35。 4■ 4
2■
24。 9■ 0
17。
042
36.700
22.03
729
■7.465
38。 ■56
22。
26。 53■
■7:853
39.708
23。 ■9
27.337
■8.208
4■ 。
340
23。
84
43.00■
24。
52
44.688
25。
29
2312■ ■
24。
25。
Ser■ es
VI
2■ .■ 53
■4。
745
46。
22。 ■86
■5。
426
48.3■ 8
23。 ■95
■6。
074
50。
24.■ 88
■6。
645
25.■ 69
■7。 ■47
26。 ■66
■7.665
20。
27。
277
■8.■ 76
2■ 。
28。
452
■8。
29。 60■
―■
496
.54
58
26。 ■3
27。
05
064
28.00
Ser■ es
VII
764
■4。
469
672
■5。
096
723
22。 688
::
■5:727
■9.224
23.684
1
■6.354
1205』
Appendix 5A. Continued.
Ｔ
Ｔ
一Ｋ
一Ｋ
Cp
」K ・ rno■
●´
24。
667
■6。
900
52。
865
29。
76
25。
683
■7。
409
54。
497
30。
94
26。 7■ 7
■7。
936
752
■8。
409
27。
28.8■ 5
・
Ser■ es VIエ エ
● ・
■8.879
■。855
1
0。
437
2.■ 0■
￨
0:033■ ■
02■ 86
079
■9。
3■ 。
356
■9.959
32.476
20。
33.608
20.84
2。
873 1
0。
752
2■ 。29
3。
■■8
0`■ ■49
353
30。
34。
2。
347
:
2.597
39
35.946
21。
75
3。
37。 23■
22。
24
3.637 1
38.6■ 8
22。
77
3。
40。 ■24
23.35
4■ 。775
24.02
0。
04620
0.06■ 23
‐
963
08798
0.■ 43■
Oe■ 90■
・
Ser■ es
0。
25■ 8
IX
670
24。
83
■。897
45。 68■
25。
76
2。
22■
47.595
26。
69
2。
539
0.05954
422
27。
66
2。
888
0。
08827
5■ .■ 76
28。
69
3。 300‐ il
0。
■359
43。
49。
ヽ
[206]
O.02422
´
0.04099
Appendix 5A. Continued.
Ｔ
Ｔ
一Ｋ
一Ｋ
3`752
0.2■ ■2
ser■ es Xエ エ
series X
●′
●
3。
0.2079
753 1
■。876
0。
02379
4.334
■49
0。
03552
4。
888
0。
2.430
0.05■ 58
5。
364 1
0.6959
795
0.08000
5.857.
0。
■1265
2。
2。
0,33拿 0
5074
9358
31240
0。
■282
6.4■ 5 1‐
3:7■ 2
0。
2035
6。
942 1
■。62■
4.222
0。 3■
76
7。
479 11
2:O■ 0
4.727
0。
4664
8。
053
2.494
0.6480
8。
668
‐
9.33■
: ￨‐
5。
208
5.726
0。
8967
Ser■ es Xエ
2603
3.999
0。
4.420
0137■ 9
4。
865
0。
3。
05■
3.686
■0。
050
4。
407
10。
8271:
5。
249
■■。657
.
6.■ 44
ser■ es XttII
5■ 97
5.309
0.6993
5.305,
5.800
0.93■ 9
5。
◆
[207]
885
O:6696
0.9489
#ie
{r:r:{.!i&'/n
Appendユ x 5Ac
Continued。
む
Ｔ
Ｔ
一Ｋ
一Ｋ
●
」K ・ mo■
・
6e467
■.284
63。 3■ 2
4■
037
■。676
64.447
43。 56
7。
′
Cp
。■8
7.629
2。
■34
65。
545
46。 53
8.269
2。
690
66.598
50.29
8。
98■
3.350
67.597
55。 57
9。
794
4。
■5■
68。 53■
63.99
10。 7■ 5
5.■ 33
69.368
8■ .77
■■.7■ 3
6e■ 97
69。
977
■83.44
■2。 75■
713■ 3
70.6■ 4
7■ .79
7■ 。593
37。
7■
72。 72■
36。
4■
Ser■ es
XIV
.259
28。
72
73.85■ 1
772
29。
66
74。
973
54.237
30。
68
76。
083 1
5■
52。
55。
673
571038
58。
373
3■
.78
36.26
36。 35
77.■ 84
36.49
36。 59
33.00
34。
Ser■ es
28
xV
59.666
35.70
54.984
3■ .26
60。 9■ 9
37.39
56。
366
32.36
62。 ■36
39e■ ■
57。
707
. 33。 64
`
1208]
…
″ =・
°
Ⅲ…
′
‐.
… Ⅲ
Appendix 5A.
・
1
・
Continuё
d◆
●
Ｔ
Ｔ
一Ｋ
一Ｋ
59.007
60。
＼
70。
362
36。
50
70。
779
43.60
7■ 。3■ 4
38。 ■2
62.396
39。
35
993
40。
54
63.58■
41.42
64.■ 57
42。
722
65.277
65。
マ●
95
38。 1■
64。
820
」K ・ Ino■
34。
6■ 。494
62。
■
269
Cp
Ser■ es
90
44.04
45。
■09。
XVI
65.486
46。 24
66。 ■■8‐
48。
66。
52
66
850
5■
3■
。3■
67.856
57。 47
47.25
68。
780
67。 32
05
69。
507
87。 06
66.352
49。
66。 87■
5■ 。38
70:021
67。
376
53.96
70。
577
70。 88
67。
867
57.07
7■ 。687
37。 57
68.339
61.45
73.2■ ■
36。 28
686789
67。 ■■
74。
670
36。 30
69。 2■ 3
75。
79
75。
930
36。 46
69。
599
90。
32.
77。 ■08
36。 67
69。
927
■24。
00
78。
274
36。 79
79。
538
37。 23
706■ 39
344:2
`
1209]
2■ 0。 0
・
sd.r
drrffii
Appendix
5A. Continued.
り
Ｔ
Ｔ
●
￨
37.49
82.255
37。
83.608
38。 ■4
960
38.63
84。
●
898
一Ｋ
一Ｋ
80。
84
86.4■ 5
39。
06
956
39。
60
87。
89.47■
40.05
90.96■
40。
55
430
40。
98
92。
Series XIX
II-I Transition,
93`880
4■ 。52
95。 3■ 0
42。
Continuous Heating
Series
XX
II-I Transition,
Continuous Heating
Seriё s XXエ
255
‐
45。
40
■52.297
.
45。
54
■50。
06
154。
Series )ffII
4961=￨ 45654
■56.833
45。
70
Transition,
■59.222
45。
78
Continuous Heating
■6■ 。654
45。
96
164。 ■22
・ 46。
02
III-II
Series XVIII
III-II Transition,
■66。
■69。 ■69‐
46。
Continuous Heating
■7■ 。750
46.37
■74。
[2■ 0]
628
370
46。 ■5
46。
33
56
Appendix 5A,
Continued。
Ｔ
Ｔ
002
46.65
■79。
627
46.8■
■82,2■ 0
46.98
806
47。 ■5
■84。
↑
■
一Ｋ
一Ｋ
177。
■87.384
47。
34
945
47。
52
■92.520
47。
70
■95。 ■■0
47.93
■89。
■97。
686
48。
200。
269
48.24
202。
886
48。
208.■ 29
48。
2■ 3.287
2■
99
49.33
49。
70
5.825
50:26
473
50.87
2■ 8。
Fus■ on
39
48.70
72■
218.982
06
205.5■ 5
2■ 0。
Series xx工 エエ
Fus■ on′
Continuous Heating
[21■ ]
50。 87
=,■ `0■・ ■●
Appendix
58.
Measured
heat capacities of DI.
Ｔ
Ｔ
一Ｋ
一Ｋ
cp
JK-1*mol-1*
Ser■ es エ
79.848
43。
92
949
43。
57
80。
6■ 。
37.53
62.972
38。
643243
40.■ ■
III-II
484
4■ 。49
Continuous Heating
66.690
42.97
672
65。
Series II
82
Transition,
865
44。
84
69。 0■ 2
46。
77
72.673
55。
79
70。 ■26
49。
00
73.662
59。
90
7■ 。205
51。
37
74。
603
65。 ■8
72。
248
54。
46
75。
490
72.93
73。
254
58。
20
76.306 :l.
74.2■ 6
62。
88
77。
75。 ■29
69.40
77.473
980
79.44
78。 ■53
67。
75。
Ser■ es
005 1
58
‐ 28■
￨
.45
79.2■ 9 1
44。
42
43162
22■ 。■6
801426
77。 84■
93.59
8■ 。74■
752
45.24
83。
[2■ 21
■20。
48
77。 28■
ヽ
66
50。
■00。
78。
85。
1
76.738
19
III
046
‐
￨
43。
56
43。
62
Appendix 5B.
Ｔ
Ｔ
?
一Ｋ
一Ｋ
-p
JK-1*mol-1*
339
43。
76
■09。
292
52.7■
85.6■ 9
44。
07
■■0。
555
53。 ■0
86。 89■
44。
38
■■■。809
54.06
88。 ■52
44。
73
■■3.055
54。
82
405
44。
94
■■4.286
55。
62
90.646
45。
38
■■5。
507
56。
28
.874
45。
72
■■6。 72■
57。
07
095
46。 ■3
■■7.924
58。
08
94.307
46.50
84。
89。
9■
93。
ヽ●
Continued.
series lv
95。
505
46。
95
96。
693
47。
40
■■9。
97.869
47。
65
■20.6■ 5 ■ 60。
99。
039
48。
24
■2■ .769
■00。
203
48.65
■0■
.449
■02。
782
■22。
446
909
59。 37
83 .
62.00
1
63.45 1
25
■24.033
65。 09
49.72
■25。 ■43
66。 39
69。 09
49。
■04。 ■06
50。
33
■26.243
■05.4■ 7
50。
83
工エーI
■06。 7■ 9
5■ 。46
■08。 0■ ■
52。 ■3
Trans■ tion′
Continuous Heating
[213]
Appendix 5B.
Continued。
Ｔ
Ｔ
一Ｋ
一Ｋ
Ser■ es
928
53.35
■24e357
64.92
■■2。 ■90
54。 22
■25.65■
67.63
446
54。 9■
■26。 9■ 6
■■0。
●
0
,
■■3。
■■4。 69■
55。
70。
6■
Transュ tion
77
922
56。 7■
■30。
892
48。
62
■■7。 ■35
57.49
■32。
682
48。
57
257
48.54
■■5。
335
58。
46
■34。
■■9.623
59。
65
■35.932
■20.993
6■
■22.344
62.58
■39.297
48。
39
■23。 67■
64。
28
■4■ .035
48。
35
978
66。
06
■26.260
68。
98
■27.4■ 9
7■ 。95
■■8。
,●
Seriё s VI
V
■24。
.05
■37。
48◆
48
48.39
602
Sories VII
Transition
■。920
O。
0246■
2。
■64
0。
03425
0。
0479■
640
48。
65
2。
408
■32.■ ■3
48。
58
2。
640
0。
06■ 93
■33.584
48.53
2.879 1
0。
08■ 88
■30。
`
[214]
.
:Ъ
+‐
´
'●
Appendix 58. Continued.
Ｔ
Ｔ
Ser■ es
IX
3。
■42
0:■ 090
3。
433
0.■ 474
■。840
O。
02076
3.75■
0.20■ 0
2。
066
0。
0296■
093
0.2708
2。
334 1 1
0.0425■
369■
2。
583
0。
05862
0。
08■ 43
3:0165
0。
■0■ 0
3.369
0。
■374
0。
■984
4。
4:464
●
一Ｋ
一Ｋ
JK-1*mol-14
4。
900
0。
014994
2ι 8■
series VIII
‐
8
:
■。9■ 5
O。
02392
3:723
‐￨
■62
0。
0332■
4e■ ■0
1
2。 4■ 4
0。
047■ 9
4.490 1
2:660
0。
06467
4。
2。
2。 9■
7
■90
0`■ ■58
3。
485
0。
‐
￨
3889
015■ 69
serios
■594
4。
583
■■
′0。 2■ 28
5108■
■
2973
5.539
‐
4。
■72
0。
4。
567
0.4066
4.999
0。
0608668
3。
3.8■ 4
872
0:2769
0。
5`98■ 1
5589
12■ 5』
Oe3994
0。
5737
0。
7709
0:9862
6。
435::￨‐
■.2456
6。
922 11・
■15683
¨″
Appendix 58. Continued.
Ｔ
Ｔ
一Ｋ
一Ｋ
cp
JK-1-mol -l
Cp
JK ・ Ino■
・
7。
472
■.9757
1■ 。240
5。
8。
107
23506
12。 ■20
6。 6■ 3
13.04■
7。
688
579
Series XI
4.707
XIII
■■.025
5。
473
0.8247
■■.988‐
6。
495
6.■ 38
■.0704
12。
925
7.485
9
■.3649
■3。
878
8。
7.■ 43
■。7302
■4.9■ 0
9.633
728
2.■ 84
166046
■0`768
8.359
2.73■
17。
226
■■。854
9`029
3。
5。
■86
5.669
6。 6■
7。
Ⅲ●
Ser■ es
0.439■
9。
0。
‐
843
Ser■ es
6■ 29
375
■8.380
4.■ 98
■9。
X工 工
■2。
563
852
587 .
■3。 82■
Ser■ es
XIV
■55
2。
553
■3.680
8。
8.978
3。
3■ 4
■5.00■
9.744
9。
698
4。
048
■6.422
■■。■23
■0。
434
4。
829
17。
8。
[2■ 6]
772
■2。
329
330
Appendix
58. Continued.
伊
Ｔ
Ｔ
●●
一Ｋ
一Ｋ
●
■9。
093
13.438
45.4■ 4
20。
380
L4.405
46。
807
27:66
2■ .6■ 9
15.291
48.232
28.33
22.828
16.065
49。
667
29.20
24.O■ 9
16.818
5■ 。■53
30。 0■
25。 20■
L7.486
52。
724
30.89
26。
420
L8.L27
54。
342
3■
27。
722
L8.792
55。
953
32。
29。
078
L9.432
57。
557
34。 ■0
30。 45■
20.L3
596■ 73
35。
32
3■ 。8■ 7
20.79
60。
769
36。
69
33`■ 63
2L.47
26。
98
.89
99
34。
527
22
35。
934
22.64
III― II TranSition′
37.327
23.25
continuOus Heating
674
23.85
40。 0■ 3
24.44
4■ 。
364
25. 05
Series )ffI
II-I Transition,
42。 7■ 9
25.67
Continuous Heating
063
26.3L
38。
44。
Ser■ es XV
.0L
も
1217]
Appendix 58. Continued.
Ｔ
Ｔ
■42。
375
■44.569
XVII
48。
30
48.33
998
48。
97
■88。
755
49。
21
■9■ 。496
49.48
■94。 22■ /
49。
59
49。
85
900
48。
35
■96。
■49。 3■ 9
48。
32
■99。 6■ 6
50.■ 2
■5■ 。806
48。
25
202。 3■ 3
50:26
■46。
●
●
一Ｋ
一Ｋ
Ser■ es
■85。
928
■54。
306
48。 ■7
205。
0■
9
50。
44
■56。
792
48.■ 6
207。
702
‐ 50。
53
■59。
283
48.■ 6
2■ 0。
398
50。
67
50。
59
■6■ 。979
48。
25
2■ 3。 ■05
■6437■ 5
48。
25
2■ 5。 9■
■67.290
48.33
■69.878
48.40
172.479
48。
2■ 8。
094
48e57
■77。
726
48.65
48.64
226
48.9■
■83。
52.89
Setties XIX
458
62。
64
Fusュ on
XVIII
■80.403
824
Continuous Heating
220。
Ser■ es
5■ 。24
Fus■ on′
50
■75。
6
223。
`
[2■ 8]
333
63.■ 8
.´
´
,‐
.
ヽ
‐
● ●
CHAPTER 6
Properties and Phase Transitions
Analysis and Disgussion
Thermodynamic
"
け●
●
1219]
6-1. General- remarks
In this chapter our object is to analyse the results
of thermal measurements on soLid hydrogen halj-des
and their deuterium analogs to see what can be Learned
about their vitirational ptop"ities and mechanism of
phase transitions. For instancer w€ should Like to
know to what extent the phase transitions can be
described in terms of successive orientationaL
●
lt
order-disorder model proposed by neutron scattering
experiments. ALthough uncertainties in some of the
auxiliary data required are so great, some conclusions
about the mechanism of phase transitions in hydrogen
halides can be drawn.
Following analysis and discussion will consist of
four parts: (1) vibrational contribution of heat
capacity and onset of orientational disorder at low
tenrperatures t Ql defect formation phenomenon just
below triple point temperaturei (3) extraction of
order-disorder heat capacity in transition temperature
region; and (4) mechanism of the phase transitionsWe will start to discuss the vibrational properties
of crystal lattice.
[220]
6-2. Low temperature region
6-2-L. Zero point properties
The characteristic temperature at 0 K
rn actual examples of insulators, it is fourra(l) that
the frequency distribution takes the form of a power
series
G(ν )=
α,2
+
4 +
βν
6 + .。
。
γν
that converges asymptotica■
■y
at
■ow
(6-■ )
frequenc■ es
ν
■ess than abOut (υ max/25)′ "here νmax is the Debye
cut-off frequency. The consequence is that the heat
capacity at constant voLume becomes
t * brS + cT7 + ... .
cr, =
"T-
(6-2,
is an equivalent series for the apparent
characteristic temPerature
There
へ
●
oD(E) = o0
tr - atforz -
B(h-) ...1.
(6-3)
In this equation' OD (T) is the aPParent Debye
characteristic temperature that corresponds to C.,
obtained from experimental data; O0 is i'ts limiting
value at T + 0 K. One connection between equations
6-2 and 6-3 is provided bY
%=(中
)VL
[22■ ]
(6-4)
・
a numerical estimate of 0O from heat capacity
data, it is convenient to plot.either C.rT-?- or OD(T)
)
against T-. If the first is used, the intercept of
the curve gives the value of the coefficient a.
Since the correction of (cp-cv) is negligibly smaLl
at T < L5 K as wiLl be mentioned below, the experimental
c*T-3
value is plotted against 12 in figure 6-1.
p
No attempt has been mad,e to estimate the coefficients
b and, c because of great uncertainty.
The temperature dependences of Debye temperatures
derived from the measured heat capacities had been
Those mean that the
shown in previous sections.
form of the lattice frequency spectrum resembles that
of a Debye spectrum. This can be accounted for by
the fact both the 2N librational and N intramolecular
vibrations are well- separated from the remainder of
the frequency spectrum. In fact, intramolecular
contribution is negligibJ-e at the temperatures measured,.
Furthermore LibrationaL contributions ban be neglected
in the lowest temperature region T
haLides. The Debye characteristic temperature at 0 K
is thus determined by assuming 3N degrees of freedom
(see table 6-1).
It is worth comparing the OO of HCl, HBr, and HI
with that of Ar(93.3 K), Kr(71.7 K) j5) and xe(64.0 x;(6)
To obtain
●
^●
r
[222]
2/K2
20
60
80 0
20
40
60
80
50
50
45
45
40
40
︲
ｏＪ 口 ¨ｏ
35
35
HI
28
６
２
26
４
２
24
２
２
22
。
２
20
旧
D Br
H Br
:8
９
ｏ／ ｏ
9
８
8
6
オ
20
40
60
移
80 0
7
°
20
Ｃ ︰
Ｄ
7
Ｃ 〓
Ｈ
へ
●
r O
だ
ξ
ヮ
40
60
80
″2/K2
FIGURE
5-L.
Graphs
of Crrr-3 against
[223]
T2.
、
ＴちＥ 寸・Ｙ つ寸︲〇一＼ ｎ︲Ｋ も
８
２
、も
Ｅ
Ｔち 寸︲Ｙ つ守ｒ〇 一＼ ｎ︲に
●′
40
「
6-1. The coefficients (a) and the Debye
characteristic temperatures at O X.(OO) determined
by the plots of c.rr-3 against T2.
TABLE
Sub,t'n,es
:
HBr
H1
‐
■8.6
+ 0。 3
34。 6 +10。 3
DC■
6.55 + 0。 ■4
DBr
■9:■
D工
牛●
■
64
6。 48 + 0:■ 4
Hc■
●
a x
3218
+ 0。 5
+ 0.6
96
T
■44。
2 +
■0■ 65
■.0
+ 0.5
82。 5 + 0。 3
■43:7.+ ■。0
■00。
6 + Oc8
84。 0 + 0.5
respectivel-y, because of their comparable molecular
weight. The rather heigher OO may come from the
molecular multipole interactions and hydrogen bonding
in hydrogen halides. I As for the discrepant behavior
between HI and DIr &DY positive explanations can.not
be put forward.
1224]
The heat
of sublimation at 0 K
in the preceeding
papers may be used to calculate the heats of sublimation
of hydrogen halides at O K. The reLevant thermodynamic
expression is
The thermodynamic properties given
Ausob(0 I().
= AHsub(r) fT
"n(gas)dr
rF
+/6"n(solid)dr+4,
(6-s)
the last term A is that of gas imperfection.
When'the critical constants Pn and Tn are given'
the term A is represented by following equation.
where
s
P
R (-)
A=
-L28 Pr
-T2
18r,?
t#)To
rr
(6-6)
of vaporization were not measured in
the present investijation, the data used are those of
Giauque and wier"(7) and clusius and wolf(8) for
Since the heats
み
●
hydrogen halides and deuterium haLides, respectively.
Unfortunatelyr rlo data for DCI are available. The
resuLts obtained are summarized in table 6-2 and the
values of rare gas solids are also included for the
sake of comparison. It is found that the multipolar
and hydrogen bonding interactions play an important
role to determine the structure of hydrogen halides.
1225]
.
■．．
ｔ．
一 一一 ・
ミ● 〓ヽ■一
・
，
，
卜
●
6-2. CalcuLation of the heats of sublimation at 0 K'
(in the unit of kJ mol-1*)
TABLE
HC■
Heat of sub■ imation
at T = Tf
.
HBr
HI
△Hち .p。 16。 ■50 ■7。 6■ 5 ■9:765
.iquid
［ＮＮＯ］
fusion
7■ o
■。
202
■。
0.922
■。97■
2.399
2。 855
, DC■
:「
-4。 828 -5。 477
c:(gas)
′ cP(sO・ id).
:「
at T = O K
5:62:
0。
△
_ Heat of sublimation
1
、
024
20。 85
711:'
0。 052
23.30
二
と
。
175
90,52
0.096
26。 52
DI
I
Ar
Kr
………… ■7。 8■ 5 ■9.732
■.945
Hs二 f)・ 1183421。 2■ 623。 542 -‐
△
撃
1∫
DBr
■.304
■.043
2。 369
2.84■
2■
.48823.6■ 6 7.78610。 79■
-1.609 -5。
4o2
6。
「
416 =■ .74■ -21496
。
636
■■ 64 ■
6。 096 8:■ 6
0.■
2.1■
■
0。 024 0。 052 0。 093 0。 042 0。 059
24。
25
27.43
7.72
■■.■ 5
r*j
-+j
-c
I
,r
,ll
The
static lattice
engrgy
It should be noted that there are one or more phase
transitions in hydrogen halides. Static lattice
energy of phase I, which wiLL.be reffered to EO(I),
was derived by anal-ysis of the vapor pressure data
in phase I, which were fitted to the formula
.n (PT3/2)= (a/T)+ b`
Thё
(6-7)
static lattice energy is re■ atedl:to a through
aNk = Er = EO(I) - Ezrlib i
WheFё =2′ iib iS lhe Zer? p01,t
The sio38 6: giapA
(6-8)
■
ibratiOna■
i・ 1
1 ln(PT3/2)aglingt
。
‐
energy。
ives
し
l
A smal■ correctil●
E. a la■ ue Of 2■ .29 kJ mo■ l for Hc.。
to thi3 va■ ue must be madё fOr thё ёffeOt of defect
fo■ .llati6h
f 21.39 kJ Ino■ 111
which ■
eaas t● a revised va■ uと 。
￨●
E去
‐
￨
in the nё ighborho9a of thё triplё point′ ‐
.ib′ Whi,h lF IS'umed t°
′
1‐
makё no difference
between phagё s tt and 工エェ′catt bё appr。 文imate■ ソ
ё予a■ uatё d
kき
from the
■ibrati6nal
mO■
・ , th,ref6re =。
「
(土
frequenciё s as 3。 64
5。 05
)is う
kJ m。 ■
71 for Ho■ .
The results are surmarュ zed in tab■ ёf13 t,7'lh'F
‐
other hydrOge, ha■ ides。
1227]
e●
:‐
by
l‐
:
‐
‐
:十 11
▼
NOxt′ we "■ ■■ evalu● te‐ the‐ Stitid lattiこ e enligジ
Of phase =ェ ェ′10(平 II)' WhiCh isl gi●
1‐
‐
‐
ー
‐‐
‐
‐
￨ 11 1
￨
6-3. Estimat,ion of static lattice energy of
(in units.of kJ mol-l)
phases.I and IrI.
TABLE
HBr
HC■
E6
∼
DC■
DBr
D工
t
8i:tr3, i3.i3r r3?:t3', i!:?1, ,trtr:33, ,31:i3,
Ez
3 . 643 3 .206 2.7 43 2 .542 2 .52L L.g4L
, lib
(rrr) 1,.349 0.949 0.772 L.344 0.941- 0.786
Ez
,trans
24.254 27.427
20.853 23.303 26.515
AH"ob(o K)
25.03 26.60 28.20 23.81 25.92 27.44
no(r)
25.85 27 .46 30.03
27 .72 30.L5
E0 (rrr)
Eo
E"
(rrr) -no (r)
,tt.rr"
t
0.82 0.86
(rrr)
AHsob (0 X)
*o
HI
o"
065
0.
o4r
1.83
0.
029
■。80
o.
2.70
039 o .o2g
static lattice energies without correction
for the defect formation are designated in
Pseudo
parentheses.
P2el
E0(rrr) = AH"oo(0 K) * Er,trans(rrr) * Er,lib.
The translational zero
point energy of phase III
(6-9)
may
be approximateLy represented by foJ-J-owing equation.
(6-■ 0)
∞
一
８
=
０
ｋ
Ｎ
９
Ezrtrans
(III) obtained, which shows l-ittle change on
deuteration, is also incLuded in table 6-3. E0(III) is
25. g5 k,l mor-l for HCr. since the difference between
E0 (III) and EO (I) may be outside the combined
uncertainties, it should be ascribed to the difference
E^U
十●
of lattice energy between phases I and III. In fact,
the value of 0.82 k,l mol--l for HCI is comparable to
-t
The E0(rrr)-Eo(r) for Hr
the AHa, of 1.19 kJ mol--.
is evidently larger than that for HCl and HBrThis result is consistent with that of neutron
scattering experiments: HCL and HBr in phase III are
isostructural but HI differs from the two, while all
the halides in phase I are isostructural. HI in phase
III apears to stabilized additionalJ.y by quadrupole
interactions and/ox charge transfer interactions.
6-2-2。
lCs―
The
ёstimation
of (CprCv)Correction
C3)i COrrection
/
千
[229]
ヽ
￨■紺
■t=ヽ 嚢無甲おヽ
Strictly speakingr w€ measure the heat capacity (Cs)
of the solid in equilibrium with its sat,urated, vapor.
The heat capacity at constant pressure C^
p may be
obtained using the foLLowing thermodynamic expression:
●
Cs ―Cp = ―Tα V(OP/dT)s
(6-■ ■)
qoefficient
and molar volume, respectively, and (dP/dT)s is the
slope of the vapor-pressure curve of the sol-id.
When numerical values for each hydrogen halid.e are
substituted in the equation it is found that C"-Cp
is quite small, being at most of the order of 0.01
per cent of C- at the triple point. We have therefore
P
neglected. this difference between Cn and C" and
assumed thern to be equal throughout the data. analysis.
where o and V are the thermal expansion
(Cp-Cv) correction
欅
●
Since the volume can be related quite simply to the
lattice parameters, theoretical caLculations are
usually done at'a constant volume. To convert our
results from Cn to Crrr we used the familiar expression:
cp
where X
-
c., = o2w/x
,
is the isothermal compresibility.
thermaL expansion and compressibil.ity data
争
・
[230]
(6-■ 2)
Unfortinatё ■y′
are‐
incOmpiete
ｔ Ｏ
ａ ｔ
●
required. Thereforer it is necessary
have recourse to the quasi-thermodynamic relation:
temperatures
Cp
(6-■ 3)
Cv =AC:T
where a constant A is given
by
(6二 ■4)
A 二 α V/xC:
C' were calculated from
equation 6-13. The numerical values of the constant A
for HCL and HBr were computed at 130 and L5O K
The differences between Cn and
●
′
respectively as follows.
Stewart have determin"a(9) afr" isothermaL PV curves
for solid HCl and HBr up to pressures of 2 x LO4
by the direct piston displacernent method.
Compressibilities were calculated to be 3-50 x 10-5
?' -'l^
)
-'t at 130 K and 3.65 x l0-qr cmo
kg at 150 K
cmt kg-t
for HCl and HBr, respectively. No reLevant data for
-1
lcg cm-o
春
●
HI and deuterium halides are available. The molar
volumes have been measured by X-ray and neutron
diffraction and volumometer techniques. AvailabLe data
were represented in the preceeding experimental sections.
The V and o at l-30 and L50 K for HCI and HBr ldere
obtained by smoothing method. The constant A was:thus
determined to be L.50 x.10-5 and L.Ag x L0-5 mol J-I
for HCI and HBr, respectively. As for HIr therefromt
[23■ 1
A = 1.5 x 10-5 mol J-l was assumed. Further, it
assumed, that A is not affected by deuteration.
●
was
in table 6-4,
and the contribution of (C^-C.,) correction at selected
Y".
temperatures is tabulated in table 6:5. In this estimation,
we assumed that the constant A has the same value for
The data used and constant A are shown
any phase.
●「
●
TABLE
6-4. The data used for evaluating the constant A.
・
v
χx■ 65 αx.04´
K 1 ・ し
m3m01・
烹 .m2kg ・
c
T
●
●
HC■
130
3。 60a
6′ .42b
HBr
■50
3。 65a
,6.■
7・
HI
1‐
′ 25.31■ 1
3■ 。71‐「
Ax■
「
」
K Lm6■
lm6i,■
ユ
m。 ■
」
'■
44。
4Jd i
46。 65d
i:56
■:49
(■
a From reference g.
b From references 10-12.
c From reference 12"
d Present results.
キ
[232]
05
。5)
TABLE 6-5.
The
(in the units
contribution
of,
(Cp-Cv) cor:iection.
of J x-l nol-l)
Ｔ
一Ｋ
●
゛
′
HBr
HC■
0.035
DC■
HI
0。
035
0.060
0。
■6
0。
28
0.37
■.■ 7
0。
53
0。
76
■。■7
■.67
■。■5
2。
00
2。 3■
3。 4■
3.54
0。 0■
40
0。
■5
0。
25
0.33
60
0。
45
0。
64
80
0。
95
■。84
■00
2:40
2。
■20
3:32
3664
■40
4。
84
0。
88
2。
27
5:78
3。
83
5。
03
2。
38
4。
26
■60
5.42
5。
■80
6。
87
5。
200
45
4。
Dエ
0。 0■ ■
059
20
■
DBr
6。
47
5。
■7
4.9■
04
6。
34
5。
58
93
8。
92
6。
40
6.97
■
●
iタ
1233]
7`53
6-2-3. Librational contribution to heat capacity
The correlation diagram for the structure of phase III
(Bb2rrn) shows that three librational modes of the four
are infrared and./or Raman active and the fourth one
is inactive. Librational frequencies of HCL, DCl' HBr,
(13)
and DBr in phase rrr were given by rto. et al.
(from Raman study and calcuLation) and by Hornig and
o"b"rg(14) (from infrared study). The'frequencies of
HI were calculated by the following relation using
●
those of HCI and HBr.
も庁
= constant
I is the moment of inertia given from reference
15. As for DI, usual mass effect of deuteration are
assumed. Frequency vaLues used are summarized in table 66. rheir contribution to heat capacity' which is listed
in tabLe 6-7, was calculated on the basis of Einstein
'l
mod,el for f,
N degrees of freedom for each of the four
z.
where
0●
(6-■ 5)
modes.
タ
[234]
^, Lr
1,.
s.
.
ar
TABLE
6-6. LibrationaL frequencies in'phase III.
(in the units of
●
Modes
●
.
cm-1^)
HC■
HBr
H工
A.
290
265
199
A2
2■ 4
2■ 2
B1
496
400
B2
2■ 8
■95
■77
370
■7■
0●
●
[235]
Dql
2o3
■52
o28
■67
DBr
194
■53
343
■5,
DI
14■
‐
■25
1 262
■2■
TABLE 6-7。
●
■ibratiOn.
К
0.0003
■
Ｔ一
Ｋ
●′
20
The contribution to heat capacity of
(in the units of
HBr
0。
0007
Hエ
,J
0。
005
0。 0■
0。 23
0.33
0。
79
■.05
60
■。47
■。86
3。
■6
3。
80
3。 35
4。 0■
■00
5。 25
6.■ 0
■20
6。 93
■40
8。 35
■60
9。 54
200
.mo1-1)
DBr
IDC■
40
■80
x-l
3
0。 0■ 8
Dエ
06■ ■
■。23
ヽ
2。
7■
26
65
3。
96
6。
5.7■
6.29
6。
56
8.96
7。
83
8.43
8。 6■
17:89
9。
48
■0。
9e36
■0。
78
■0。
54
■■。49´
■■。80
■2。
58
■3.20
●●
●
1236]
■0。
86
22
■2。 ■9
■■。35
■■。43
■3.■ 4
30
■2.35
■3。
83
07
■4。
34
■2。
08
■0。
■3。
■4.73
6-2-4. The temperature
The comparison of Oo (T)
●
o,
.o
dependence
of
0o(T)
It is often useful to describe the heat capacity of
solids in terms of the Debye theoryr ES in this way
we may exhibit clearl-y small differences in the type
of temperature dependence of the heat capacity for
different substances. What is done is to examine the
temperature dependence of apparent Debye characteristic
temperatures corresponding to the lattice heat
capacities. Deviations of 0o from a constant value
are interpreted as being the result of departures of
the actual frequency spectrum from the assumed Debye
spectrum. It has become clear from the theoretical
work of Blackman and oth"t=(l5) that, if vibrations
remain harmonic, 0D should be constant at very J-ow
(r 6 OD,/100) and at very high (T i OD/z) temPeratures,
and should often have a minimum value in between.
Figure 6-2(a)'r,(f) are graphs of OD(T) as a function
of temperature for hyd,rogen and deuterium hal-ides.
In the calculation of the plotted points, (Cp-Cv).
correction and librational contributions were
subtracted. In each graph, broken line shows the
extraporation by means of the Thirring expansion.'(17)
The decrease in 0o(T) in the region T
obserired for some simple crystals(18'19) and has been
:
●
[237]
Ｌ
。
。
﹁
れ鼈。
150
￨・
140
130
Y
●「
S
I
°
°
。
6θ
o::°
も
°
も
・
°
び
電 5。 o:。 。
°°
°・
。
,。 。
iσ
3dび ')´
120
＼
ぬ
0
(a)
150
・●
.
′.
、
140
130
120
″●
(b)
0
10
20
30・
40
50
戸 /K
6-2. The temperature dependence of 0D.
Broken lines show the extrapolation by the
Thirring expansion. (a) HCl; (b) DCl.
FIGURE
[2381
・
0
亀喝喰爵♂ぼぼ“゛
…
5観
‐
瓦「
=再 耳
Ｙ＼
口
ヽ
●′
●
20
″●
30
万/K
6-2. The temperature dependence of OO."
Broken l-ines show the extrapolation by the
Thirring expansion. (c) HBr; (d) DBr"
FIGURE
1239]
ウ
90
80
70
０
９
●
Ｓ
Ｙヽ 一
●「
70
60
●
●
0
10
20
'30
.40
50
万/K
FIGURE
6-2. The temperature
dependence
of
0D.
Broken Lines show the extrapolation by the
Thirring expansion. (e) HI; (f) DI.
[240]
ascribed to the onset of anharmonicity in the lattice
,
.€s
r
moreover,
the onset of phase transition begins to overJ-ap at
this
temperatuf,€.
While the general shape of the OD(T) curve is rather
simiLar for aLl- the halides, there are differences
in detail. The curves of hydrogen and deuterium
halides are compared on a reduced. basis using OO val.ues
in figures 6-3 (a) and (b), respectively. Also shown
for comparison are the curves for argon and krypton.
An inspection of the figures reveals that the curves
' for HCl and DCl show a more pronounced minimum at
T = 00イ ■
9 in ,Ontrast tO f■ atten‐ off behavi6r in H工
″
and D工 between T = 06/10 ald 06/4.
03(T)19urveS
Thё ‐
of HC■ and HI obv■ 9us■ y change by deuteratio.61
We bO■ ieve that this ■sot6pe effectl ilta re● ュ o■ e
a■ th6ugh
0●
thё re are some uncertainty.￨■ lhe‐ ■ェbratiOn
l
freq■ ency。
■
:￨￨ ￨111‐
￨￨￨
‐
‐‐
‐
■
￨‐
l
‐
‐
The determinal■ Oh 01 0∞
of lattice heat capacity
converted into the form
derived, by Thirrinn(t7) t
"
of the corresponding Debye characteristic temperature
The high temperature expansion
by
■
Domb
031〒
and Sa1t"t,
(21)
Ol[1-■ 器)2+B(等 )4_■ 1■ ￨116二 16'
・
124■ ]
￨
●
￨
￨
￨
￨
￨
￨
￨
￨
l
:。
0
９
０
。Ｓ ＼ 。ヽ
ＬΓＩＩ
0。
8
0。
2
万/Q
●
トト
FIGURE 6-3.
The temperature dependence of OD °
a reduced basis using each
, HBri ?"""t
, Kr.
[242]
,
00。
H工
,
' ,
(a)=― ―――ニー ′HC■
ニニ
・
―・
-0-′ Ar′
)￨“
￨￨■ ′
ヽ
、
`.4ツ
‐■●
ヽヽ=‐
￨｀
″￨
●
９
０
ｏＳヽ﹁も
0。
2
戸/′ Q
ミ●
FIGURE 6-3.
The temperature dependence
a reduced basis using each
′ DBr,
′
・
●
・・
o・
OO. (b)
of
0O on
DCl;
・―-0-二 ′ Ar,
・・・ ′D工 , 一―。一―
・
Kr。
:
[243]
-r
'
t-t
Of, against
T-2, which is shown in figures 6A(a)ru(c), gives the vaLue of 0- from the extrapolation
The plot
of
-) = 0.
Eo T'z
values obtained are summarized in
table 6-8. In folLowing sections, the heat capacities
corresponding to this extrapolation curves will be
The
Ooo
used as the normal lattice
TABLE 6-8.
0:aし ,・
・
The O∞ Value,19btainё d from the p■ ots of
St i「
2.
￨
HC]" HBr HI
0ノ 率
Part.
■32。 3 9■ .5
‐
DC], DBT DI
7313 ■35.1 92.076:5
[244]
..
i
l,
ざＱ＼智
Ｎ
●
５
。
８．
８．
ｏく 巻
ヽ一
８
６
４
。 。 ５
５
５．
ゝЪ ＼智
0●
5.2
Graphs of
●′D9■ 。 (b)0′ HBr,
２ Ｄ ′
０ ●
FIGURE 6-4.
●0
0
[245]
aga■ nst T
DBr。
(c)
-2
0′
(a)o′ HCl,
HIF
● ′ DI`
6-2-5.
of orientational disord,er
The observed heat capacities in phase III can be
●
Onset.
represented by
Cn(obs.) =CL*Ctib+
where C"
●「
0
0●
(Cp-Cv) +AC
(6-■ 7)
is the lattice heat capacity corresponding
to the Debye temperature evaluated by Thirring
extrapolation. The terms of CrtO and (Cp-Cv) correction
have been al-ready estirnated in the preceeding sections.
Excess heat capacity AC, that is, the Low temperature
tail of the transition, was then computed by equation 5L7 and iLlustrated in figure'6-5. The onset of
transition and anharmonic effect in the Lattice
vibration seem to appear at the same temperature.
The temperature at which the transition begins to
occur is found to be in the order of the transition
temperature except for DBr.
It is possible to estimate the energy required to
reorient a molecule, from the low temperature tail
of the transition. Assuming that the number of
molecule (n) in the wrong orientation in ordered
matrix is very small compared with the totaL number
of the molecuLes Nr w€ n.rr.
〓
Ｎ
ｎ一
exP(S/k)exP(― ε/kT)
い
[246]
(6-■ 8)
●
￨
Ｌ Ｅ ■ っ ＼ もく
●
φ●
戸 /K
FttGURE 6-5.
The
transュ tion。
▽′ H工
■ow
temperatllre
ta■ ■
of the
■owest
0′ HC■ , ● ′DC■ , △′ HBrF ▲′ DBr,
F ▼′D工 .
●
[247]
where e
AC
is such an energy and the excess heat capacitlz
is given
△
C・
by
112
F71tt exp(S/k)exp(―
c/kT)
・
(6-■ 9)
A plot is made of tn(r2ac) vs. T-1 in figure 6-6.
straight Lines are obtained at lower temperatures'
the slope of which gives e summarized in tabLe 5-g.
Good
●
6-9. The energy required to reorient a molecule
estimated from the low temperature tail of the
lowest transition"
TABLE
HC■
'o
C/k」 m。 ■
・
2。
6■
HBr
HI
DC■
DBr
D工
■。
90
2。 20
4。 04
■.44
3.65
`
"
t2481
●
10
Ｅ ｏＥｘっ＼ｋ Ｏ ｇ 三
2
234
T4
/
lO-2 K-l
of ln(Ac 12) against r-1 for the
J.ow temperature tail of the lowest transition"
(a) o, HCl; A, HBr; V' HI.
FrcuRE 6-6. Graphs
Ｊ¨
t24e1
0
５Ｅ Ｘっヽ ＮＬ Ａ く ︶Ｉ
ｒ︲
10
，
2
‐
3
4
戸J/10・ 2K‐ !￨
0●
F工
GURE 6-6.
th6
■ow
Graphs of
■n(△ C
T2)againSt T ・ lor
temperature tai■ of the
(b)o′ DC■ , △′ Dpr: ▽′D工 .
●
[250]
■owё st
transitione
reflects the interaction energy with
neighbors, it is r'itorth noting that the values for
both bromides are smalLer than those for others.
The magnitude of e corresponds to the difference in
energy between a certain orientation specified by the
space group and another one of twelve orientations.
The d.eviation of the points at higher temperatures is
due to rapid increase of the heat capacity in the
transition region. It may be due to an increasingly
larger interaction between ltrong orientations.
Since the e
●
0●
●
[25■ ]
●
6-3. High temPerature region
The formation of vacancies in a solid near the meLting
temperature can contribute to the heat capacity.
In fact, the observed heat capacities show markes
upward trends in the temperature region below their
melting points. The excess heat capacity due to
vacancy formation is
喝=(や
●
(6-20)
'p
n" is the number of vacancies and h" is their
enthalpy of formation. The number ns is given by
where
ns = NA eXP(Ss/k)ettp(― hs/kT)
(6-2■
)
is Avogadro constant and "" is the entropy
of formation. Analogous analysis was already made
in the case of orientationaL defect formation in
section (6-2-5). The enthalpy of formation may
therefore be obtained from the slope of a plot of
2 aga,inst T-1. Before applying equation 6-20,
'
ln (AC'T-)
the contribution from impurities, which may produce
a pre-melting rise in the heat capacity' ltas subtracted
where No
0●
by
ai*n = x
0
where
R
*7"
'12
/ (rf-r)-
(6-221
x denotes the mole fraction of the impurity
[252]
、
Tf is the meLting of pure substance. The resuLting
enthalpies of formation of vacancies, which is
summarized in table 6-L0, are found to be about one hal-f
of sublimation enthal.py values at 0 K for a1l the
hydrogen halides, in contrast to two-thirds for Ar
or Kr. For the sake of comparison the enthal.pies
of self-diffusion in phase I obtained by NMR method
AH(NMR) are included in table 6-10. The vaLues of
AH (NMR) are in good agreement with those of AH",rb (0 K)
rather than hs . The facts indicate that the NIvtR
can observe the energy barrier required to remove
a molecule from the lattice. Howeverr a comparison of
h" and AHsub(O K) obtained by calorimetric study.
ind.icates that reLaxation of surrounding molecuLes
into a vacancy is J.arge" NMR can not see this relaxation
and
`
む
phenomenon.
●
●
●
[253]
●
6-L0. The enthalpy of formation of vacancies
and the ratio to heat of sublimation at 0 K.
TABLE
HC■
HBr
‐■
0.45 ■
■
。
8五
瀞
DC■
84 1■
12。
h
s
△Hsub(O
AH
..-..
K)
。‐
17116
:°
o.5o o.5l o.4g
-J- 20.85 23 " 30 2;.sz
8。 4b カ
■
ラ.6°
AH (NMR)
-..----='
kJmol
DBr
25。
5d
16.3d 2s.gd
a Present results
I^
*' From T, of H (Krynicki et aI. )
c From line width of H (Okuma et aI.)
A
ct From Tro of H (Genin et al. )
e From T, of H (ltorris et al. )
f From line width of H (Norris et a1.)
:
[2541
11。
91
o.5L
.25 27 .43
24
23.4c 23.0f
つ
.D工
0.51
(O K)A
kfmol
0●
HI
6-4. Transition temperature region
We evaLuated the contribution to heat capacity of
crystal Lattice and vacancy formation at lower
temperatures and at higher temperatures' respectiveJ-yIn this section, the nature of successive transitions
will be discussed.
When the rotationaL mol,ecuLar motion is treatedt
two extremes are possibl-e: the molecuLes may rotate
0●
essentially freely in the crystalr €ts is supposed
to be the case for the sol-id hydrogens' or the
rotational motion may be completely restricted and
hence transformed into vibrational motion (libration).
Whether either of these extremes or some intermediate
situation pertains shouLd be determinable by experiment
but rarely seems to have been established unambiguously.
Our analyses for phase I will be made by assuming
that the moLecules librate with the same frequencies
as those in phase III. The bases for this are as
follows. (i) The observed heat capacities in phase I,
such as 5R at 110 K in HCI, are too large to be
explained as free rotational and even as librationaL
motion. (ii) The observed difference in heat capacity
between HCI and DCI- is 3.2g .I K-l moL-I, which is in
good agreement with 3. L9 ,f K:'1 moL-l caLculated by
using LibrationaL frequencies in phase III"
●
[255]
●
(iii) Since the corresponding isotope effect in HBr
and HI is larger than what one would expect from the
difference in the librational frequency, some other
factors than the motional (librational- or rotationaL)
contributions will have to be tonsiaered.
.\
6-4-L. Extraction of anomalous part of
at the transition
Cn
The observed heat capacities should be represented by
Cn(obs.) =CL*CLib*
(Cp-cv)u+Cd*Ct" ,
(6-231
where (Cp-Cv)N is (Cp-Cv) correction of normal part'
which can not be directly observed in this case.
CU is the heat capacity for the defect formation
0●
(6-3). The Cr, is the
referred to as AC^
p in section
transitionaL part of heat capacity at constant pressure.
The corresponding enthalpies and entropies can aLso be
given by
H{ObSO)= HL + H■
ib
十
ナ
1Hで ,b-9v)N
Hd
す
Htr
′
(6-24)
and
s(obs.) = sL * stib * t{"n-"rr)* * sd * st,,
(6'25')
An attempt to estimnte (CP― C↓ )N Wa, made by a,sulning
●
[256]
that the obsё rvё d
0
ic■
α′V′
and
χ
at
■30
and
■50
K for
and HBr respective■ y atte aseribedltO thosё Of
norma■ ■atticeo
‐
‐
Therefore′
(CPTCv)N=A・ iC:′ N
・
.
(6-26)
.
where
｀T CL + C■ iも ・
'v′
The Constantё
●
A・
(6-27)
‐
￨
determined for HC■ and HBr are
:￨ ￨￨￨
tive■ yO
6. j―
0 5 島
1 ■
・ ′lespと こ
・
2。 7 x ■
0 5 rno■ 」 。
for HI was assumed tO bι ‐
0 ' ana 2.フ
3.O x‐ ■
The A・
,le 961r99ti。 ■°
= (,p19キ
mputё d at se■ ected l
・
l
tempeFatureS as sh6m i■ 'N
Wlre
C°
・ 19p.CV)N esselti'・・ γl
tab■
, 6「
1■
l
diff,rこ fr。 嵐(CplC↓ ‐
9Va.laled in Sё Ction (6-2-2)in
￨
terms both of thё abso■ ute va■ ■e land lf continuity atl . 1‐
trans■ tion po■ nte
The contriPutiO'7′
Cllヽ
191l C11・ ￨′ ￨(Fも
‐
Cdf and Ctr′ are l■ ■ustFated for lC■ ′
車Br′ and Hェ ,inl l
‐
l l
,●
figures 6,7(a)′ (b)′ and (C)′ respectively.
[257]
:￨￨
‐ ‐
￨ ‐‐
TABLE 6-■ ■.
ゆ
The contribution of
(itt the tttits of J K・・ mo■
Ｋ
Ｔ一
HC■
HBr
(CbT'↓ )N C9rre,キ
・
)
DC■
H工
101.
DBr
D工
20
29
43
47
0.6■
0.97
■。■2
■。4■
■.92
■188
■。95
2:35
53
40
0。
60
0。 8■
0195
■6■ 4
80
■。52
■。64
0。
0。
0。
3■
0。
■00
2。
38
2:46
2.8■
2.93
2。
89
3。
■20
3.33
3138
3.78
4し
04
3。
89
4.40
■40
4.63
4.36
4.78
5。
20
4.9■
5.44
■60
5.44
5`38
5。 8■
5。
94
6.47
664■
6.84
6。
98
7.50
■80
7388
200
,●
[258]
36
8.5■
60
︲
、
︲
︲
セ っ＼ 、
■ ｏＥ 一
ｄ
0
Ctr
40
(C
■
v)礎
cna
20
CL
(a)
0
o
50
100
i50
戸 /K
0●
FIGURE 6-7。
C■
ib′
The contribution of leal C,paCity cL′
(CP=Cv)N′ Cd′ and 9tr.(Sё e text)。
●
[259]
(a)HCl.
′
`
０ ０
４ ２
Ｙっ＼ も
■ｏＥ一
︰
60
100
万/K
■●
F工 GURЁ
C■
6-7.
The contribution of heat capacity cL′
it' (CP二
The base
Cv)N' Cd′ 'ld Ctr (S'e teXt)e
■ine
for
エエエーエエ
0
[260]
(b)HBF・
transition is inc■ uded.
０ ０ ０
６ ４ ２
Ｙつ ＼ も
︲
ＴｂＥ 一
Q
碑 嘔必
100
150
万 /K
"●
FIGURE 6-7.
C■
ib′
Thё
contribution Or heat Cap●
(Cp Cv)N′ Cd′ and Ctr (See teXt)0
The base
■ine
for
エエエーI=
●
[26■ ]
city CL′
(C)H工・
transition is inc■ uded。
●
●
6-4-2. The III-II phase transition
An inspection of the observed heat capacities revealed,
that the III-II transition part of HBr, DBr, HI, and
DI couLd be separated from the other parts.
To determine the exces.s heat capacity, enthalpy, and
entropy contributed by the III-II transition, a curve,
which is included in figure 6-7 and numerically given
in table 6-L2, was drawn tangent to the heat capacity
curve below and above the III-II transition"
The enthalpies and entropies determined, whose
uncertainties come from those in base Iines, are
shown in table 6-13. It may be evidently claimed that
the III-II transition has the entropy of R 1n2.
This result is consistent with the structural model
of phase II prpposed by neutron scattering experiments:
Each molecule has two equiLibrium orientations with
equal probabiJ.ities.
ヤ●
●
[262]
6-L2. The base val-ues of heat capacity for
(in the units of J x-l mot-l)
the III-Ir transition.
TABLE
●
Ｋ
Ｔ一
●
HBr
DBr
Hエ
DI
40
20。 4
2■ 。6
22。 8
24。 3
50
23。 0
25。 ■
25。 8
28。 4
60
26.0
28.7
28。 8
32。 4
70
29.4
32。
32。 ■
36。 4
80
33。 3
36.7
35.6
40。 4
90
37。 9
4■ 。4
39.3
44。 3
■00
4362
46。 9
43。 4
48.4
■■0
50.5
53。 6
48。 7
53。 0
5
●●
●
[263]
TABLE 6-■ 3:
●
The entha■ py and entropylof the ==工・ II
transition.
△H..ェ _ェ
Jm。 .
ェ
■
HBr
・490上 ´
■0
DBr
497 +
HI
.
382 +
。SI工 エーエエ
.
:K ・
mo■・
5。 77主 002
■0
5.77 + 0:2
■0
5。 75 + 0。 2
●
D1
424+10
5.80+032
R 1n2 = 5.76
0●
●
｀
[264]
J x-l mol-I
6-4-3. The thermodynamic properties of the transitions
Thermodynamic functions of the'transitions were
computed
as fol-Lows.
Heat capacity
Figures 6-8 (a) and (b) show the heat capacity Ct, ""
separated out i.n preceeding section for hydrogen
halides and deuterium halides, respectively.
It can be seen that the heat capacities in phase I
are large in magnitude and converge to zero at higher
temperatures. This int,eresting result is a conclusive
evidence of the existence of short-range order above
the transition temperature. The negative vaLues of
Ct, for HI and DI probably come from the poor
estimation of the (Cp-Cv) N.
Enthalpy
,●
the transitions
are plotted in figures 6-9 (a) and (b) for hydrogen
halides and deuterium halides, respeciively.
The corresponding enthalpies through
Entropv
The results obtained are summarized
(a) and (b) for hydrogen halides
in figures 6-10
and, deuterium
respectively. The entropy associated with
●
[265]
halides'
expansion
`
曇
ＴｂＥ ＴＹつ＼ も
10
100
0●
150
万/K
FIGURE 6-8(a)。
transitions.
Heat capacities assOciated with
0′ HC■ ,
△′ HBrF
▽′ H工
.
Dashed and
dot― daShed ■ines
shOw the high temporature ta■ ■s
of SchOttky heat capacity with g./g。 ■ ■■ for
●
c. = 2 and 2。 5 卜J
Ino■
・
′respectiヤ el'。
[266]
￨
ざ
立 っ＼ ｔ
■ｏＥ一
●
100
●●
万 /K
FttGURE 6-8(b)。
transitions◆
Heat capacities associated with
。′ DC■
dOt― dashed ■ines
, △′ DBrF ▽′D■ 。
Dashed and
show the high temperature ta■ ■s
Of Schottky leat capacity with g./gO
●
e. = 2 ald 2.5 kJ Ino■
・
[267]
′respectivo■ y.
■■ fOr
J
l
プ´ i
/グア
2.0
r多
5
０
ノ
／
ご
七Ｅヱ ＼﹂
・
!。
く
/
5
︱
0。
0
50
ノ
0
︱
/
″
￨
′:50
:00
200
250
万 /K
0●
￨
￨
FIGURE 6-9(a).
Entha■ pies through the transitions,
一――――――′HC■ , 一
=―
0
[268]
― ′ HBr, 一‐
―‐■‐
―′HI・
_.__^
ヽ
“
/
//デ「
2.0
r七
fイ
ジ
‐
丁:T‐
｀
ン
5
ノ
／
０
﹂
一
ＴもＥ つこ＼ ミ
:。
/′
︲
0.5
′
ノ
0
0
:00
50
150
200
250
￨
万
￨
/K
・
†
FIGURE 6-9(b).
′ DC■
口ntha■ pies
,
二 ― ― ―
″
[269]
thrOugh the transュ
′ DBrF
― ‐二 ‐二 =■
′ D工
ti6ns。
.‐
R ln12
20
「1,牙
′%
﹁ １ ／１
15
50
︶
／
0
影η︲︲トノ／
メ
ノ
／
0
:00
150
万 /K
200
‐
じ
し
Ｆ
ｌ
︱︱卜ｂｒ
Ｉ︰
ィ ︲︰ ︲ ′ ′
０ ５
﹂
立 っ＼ げ
■ｏＥ 一
●
L´
F工 GURE
6-■ 0(a).
transitiOns.
Entropies associatё o with the
′ HC■
― ‐― ‐― ‐― ′ HI.
″
[270]
,ニ
ー
T■
′
HBF:
250
´…´
―
■ト ー・
―
R ln 12
20
‐
‐
二
フ
丁
■
11
︲ ︲
， ノ
︱ ︱ ︱ ん
︲
げ
Ｅ一
立 っ＼﹂
■ｏ
15
′
力え
０ ５
0
o
50
100
!50
transitions。
‐
/K
「
FttGURE 6-■ 0(b).
200
Entropies associatё d with the
′ DC■
一 ‐― ‐― ‐― ′ D工 。
F
― 一 二 二
r
[27■ ]
′ DBr,
250
t
of the Lattice is not easily separated from that
resuLting from the order-disorder transition, but
it will be a small fraction of the total excess
entropy. The value of R lnl-2.is marked in the figures.
They showed that the entropy converges to R 1n12.
One can relate this entropy value to the structural,
model: Phase I at high temperature limit is the
tweLve-fo1d d,isordered ntodification of molecular
orientation. The short-range order just above the
highest transition was found to be 37 , 24, and 13
per cent of R Ln12 in entropy for HClr HBr, and HI,
respectively (see tabl-e 6-14), It is noteworthy that
0●
ratio of the. short
of R ln12 just above
The
TABLE 6-■ 4。
to the va■ ue
Fange order
the‐ highest
trans■ tion.
HC■
0。
37
HBr
HI
0.24
0。
■3
り
[272]
DC■
DBr
0。 3■
0。
■4
D工
0。
06
●
.o
the amount of short range order persisting after
destructionofthe1ongran9eorderisquitelarge
especialLy for HCl.
rn this connection the work'ot pomu(22) of rsing
models in magnetic system is rather instructive.
He points out that the fraction of the total magnetic
entropy gained above transition temperature increases
as the coordination number r z r decreases" This result
is cl-earJ.y reasonable since in the Limit of infinite
coordination al-L order must be long range in character,
whereas in the limit of zero coordination only short
range order is possible. on the analogy of this,
we may conclude that the transition in HCl is, in large
part, of the one dimension and then in phase I there
ii a considerable local order with the zLg-zag chains,
which may probably fluctuate both in time and in space.
6-4-4. Local order in phase I
Analysis of configurational heat capacity
As analyzed above, the configurational- heat capacity.
in phase I is finite and asymptoticalLy approaches
zero at high temperatures. To see the convergency
of heat capacityr a pJ.ot of J.og Ca, against log T
was made as shown in figure 6-11. Dispite the J"arge
uncertainties in (Cn-Crr)pr it can be seen that the
や
[273]
￨.0
ヽ
ヽ
。
`
△
ヽ
ヽ
ヽ
、
ヽ、
、
ヽ
、
一
9
、
ゝ
８ ′ ７ ６
０ ０ ０
０
Ｃ︶
Ｅ一
︵
Ｙつ＼﹂
２
■ｏ
卜
t
ヽへ
0。
・
一
へ
、
ヘ
＼
ヽ
ヽ
、
、、
ヽ
、ヽ
ｏ■ ミヽ
ヽ
、 ヽ
ヽ
、 ．
ム、
ヽ
、
ヽ
、
ヽ
ヽ
ヽ
ヽ
ヽ、
ヽ
ヽ
＾
ヽ
、
ヘ
●●
0。
5
2。 1
20
2。 2
2。 3
log(戸 /K)
6-11. Temperature dependence of heat capacity
with local order in phase I. o, HCl; t t DCI; A, HBr;
L, DBr; V, HI; l, DI. Dashed and d.ot-dashed lines
FIGURE
ケ
tails of Schottky heat
-1 |
capacity with 91/99 = 11 for El = 2 and 2.5 kil molshow the -high temperature
,
12741
for HCL and DCL d.iffers from that for
HBr, DBr, HI, and DI. While the Ca, of the formers
varies to the power of -(0.5+0.15) of temperature,
the latter's varies to that of. -(2.0+0.5).
The obvious interpretation of a t-2 term is that
it is the high-ternperature tail of a Schottky anomaly.
An effect of this tyPe can arise whenever there is
only a limited number of closely spaced energy levels
availabl-e to the system. When kT is much greater
than the energy differences of the Levels, they
convergency
remain ef fectiveJ-y degenerate; when kT becomes
to the energy differences, the change in
the distribution over the energy Leve1s begins to
have a marked effect on the thermodynamic properties
and results in the onset of an anomaly in the heat
capacity. We will analyze the local order in phase I
in terms of the Schottky's model.
Suppose there is a system in which the particles
can exist in a group of two levels, separated from
the ground state by energy eI and with degeneracY 91.
Then the Schottky heat capacitY is
comparable
″●
CSCh=(平 )(輩
exp
)
[1
θ
[275]
(
e,/kT,
+ Go/srl exP er/rrlz!
(
(6-28)
At high temperatures (er,/kr << L) the equation
6-28
becomes
Csch = RgOg.(gO+g.):2(c./kT)2
(6-29)
= I and 91 = LL are given for the molecuLar
model as wilL be proposed below, the high-temperature
tait of Schottky heat capacity are plotted in figure 6-8
for .L = 2 (dashed Line) and 2.5 kJ mol-l (dot-dashed
line). It can be seen from the figure that the
absolute values of heat capacity and temperature
dependence for bromides and iodides are explained
by the Schottkyrs model with g7/gg = 11 and 61 =
2'v2.5 kJ mol-l. However, the behavior of chlorides
is peculiar and will reguire a different mod,el.
when 90
Possible mod.el on the rnolecular point of view
*o
will transLate the SchottkyIs modeL discussed above
into the model on the molecuLar point of view.
We
As proposed by neutron scattering experiments,
a molecuLe in phase I has twelve possibJ-e orientations
so that a hydrogen bond can be formed. The moLecule
in phase III prefer a certain orientation among them.
The configiuration, has an ad.ditional stability with
the dipolar and/or quadrupolar interactions with
neighboring molecules r &s theoretical-J.y pointed out
´
1
・｀
[2761
‖
￨
,rt?l
￨
by Hanamura.\"r In phase I with Local order, therefore,
one can assume that a certain orientation has a lower
orientations. Although
the energy difference (er) is.not identical for eleven
orientations, the assumption of gl = 11 can be used''
as a first approxirnation. The resul.ting-L er (2N2.5
kJ mol-1*) for bromides and iodides is the same order
of magnitude as the energy required to reorient
a molecule in phase III as estimated in section (6-2'5).
This fact indicates the val.idity of the model that the
subsidiarlr' 11 minima have energy e, relative to a
principal minimum in orientation. On the other hand'
the model for HCl and DCI can not be simply acquired.
It is evident, however, that the local order is
consid.erably retained and is not "thermalJ.y!' destroyed"
energy than other eleven
NMR
ら●
technique can aLso see the energy required to
reorient a molecu1e. However, the values obtained
(4.6 and 4,L J mol-l for DBr and DI respectiveLy)
are about twice those obtained by the present thermal
study. This descrepancy can be explained by the fact
that NMR detects the energy barrier between two minima
instead of the energy difference between them.
[277]
●
6-5. Mechanism of the phase transitions
In this last section, the phase transition will
again considered on the basis of the results of
thermodynamical analyses. As
resuJ-t, one can
"a
approach the mechanism of the phase transitions
be
ユn
hydrogen halides.
●
6-5-L. The disordering process
The third law of thermodynamics for hydrogen halides
and deuterium halides were verified by Giauque and
wiebe(7)'rrra by clusius and wolf IB) respectively.
The fact ind.icates that the phase III at 0 K is
perfectly. in the ordered, state" On the other hand
●9
our anal-yses from the two angles, vi,z., heat capacity
and entropy showed that the molecul-es in the phase I
at infinite temperature have l2-fo1d orientations with
equal probability in the perfectly disordered state.
To ensure this mod.eL, the entropy in the liquid phase
wiLL be considered.
in the liquid phase
The entropy gain between triple and boiling points,
which will be referred to as triq, are shown in tabte 615. Their correlations in magnitude are HCI>HBr>HI
and DC1>DBr>DI. The entropies associated with fusion
The disorder
●
[278]
辮一
一
‐￨
や
I
TABLE 6-■
｀
The entrop■ es associated w■ th transitions
and fusion and the entropv gains in
be■ ow
str
△sf
S■
q
土
■■quid
phase
(in the units Of‐ J K ・
boiling point。
DC■
DBr
7。 ■7
■8。 7■
■9。 ■0
■7。
47
2■ 。■2
39
■2。 86
■2.83
■2。 28
12.76
■2。
87
6.■ 3
1◆
■
1074
,。 66
4。 ,5
0■
ノ
・
)
Dエ
HBr
9°
HI
InO■
HC■
■2。
20.52
83
them. On the other
hand, the St, in the solid at the triple point is in
the order of HCI<HBr<HI, although it is DCI<DBr>DI
in deuterium halides. The relations mentioned above
qualitatively suggest two interesting features
concerning the disorder: (i) The local order can not
be destroyed on fusion. (ii) The local order that
remains in the liquid state at the triple point will
thereafter be destroyed on warming throughout the
J-iquid region up to the boiling point. (iii) The
overall entropy, i.e. the sum of Str, ASg' and Sr1n. r
will then represent the total magnitude of order to
A.S,
0●
5。
are approxirnatel-y equal
ヽ
●
[2791
among
be destroyed. This, however, is not uniform in the
◆
series of HCl, HBr, and HBr; the difference probably
accounts for the difference in other degrees of
freed.om of motion in the liquid state.
of disorder in solid phase
As mentioned above, the crystal cooperatively and
thermally gains orientational disord.er on heating,.
As for the process of d.evelopment of the d.isorder,
(25) d.iscussed
s6ndor et al . Q4) and Hoshino et al .
the case of DCI interms of mean square angular
displacements .0lrra> ana .o?rrt. .03ot> which represents
the molecular motion preventing the development of
zkg-zag chains in the ab plane increases rapidly above
The development
K, while .Q?rrt shows no appreciable change with
temperature. This anisotropy of molecular libration
in chlorides despite the cubic synunetry may cause
a peculiar behavior of the local order'heat capacity
L23
￨●
in phase I of HCl and DCl.
1
The structure
of phase I'
structural investigation was made for the phase Ir
of HBr. Our thermodynamical analyses, however,
suggest that the structure can be supposed to be
tetragonal system with 4-fold orientational disorder
No
苺
[280]
,
`●
in the ab plane because of its entropy value Sa, of
about R 1n4 (= 11.53 J K-l motlI1. As for the phase
Ir of HCl, it is a question of existence of the phase
itself. ShouLd a transition without an anomaly in the
heat capacity, if. it ever exists, be referred to as
a phase transition ? It is hoped to straighten out
some of the experimentaL confusion in neutron
diffraction studies themselves that exists in
connection with "L20 K transition".
6-5-2. Phase transitions and molecular interactions
In the preceeding sections (6'2-5) and (6-4-4') ,
the energies required to reorient a molecuLe were
obtained from the anaLysis of heat capacity in phases
III and f, respectively. When a molecule is reoriented,
the molecular interactions with neighbors should
change. The energies, therefore, should be related
to the molecular interactions. Hanamura evalu"t"d(23)
the dipolar, quadrupolarr. and hydrogen bonding
interaction energies between the neighboring molecules
in hydrogen halides. Further, stability by arrangement
of zLg-zag chains was discussed. Now, since the hydrogen
bond is reserved by the 12-fo1d orientations of
a molecule, the relevant molecular interactions may
be of dipolar and quadrupolar. Table 6-16 shows the
■
[28■
1
6-16. Values of dipole and quadrupole moments
and, the interaction forces between the neighboring
TABLE
ロ
- molecules.
HBr
HC■
o
‐
Hエ
u x 1018 esu cm
e x lo26 ""o .*2
1.07 0.788
3.8 4
0.382
Dipolar interaction
x to-14 erg(molecuLe) -1
1.99 0.92
0.19
Quadrupolar interaction
L.4
1.9
l-.06
x to-14 erg(molecure)-1
Hydrogen bonding
energy 42
x to-14 erg(morecule)-1
,o
●
t2az1
26
6
the neighboring molecules
cal-culated by Hanamura: the order in magnitude is
HCI>HBr>HI for dipoLar interactions, while it is
HI>HC1>HBr for quadrupolar interactions. since the
energy to reorient a molecule derived from the onset
interaction energies
中
between
of orientationaL disorder in phase III showed the
relation HI>HCJ->HBr, the responsible molecular
interactions may be quadrupolar. On the other hand,
the analogous energies in phase I are equal- (2't'2'5
-1
for bromides and iodides. The related
kJ mol-r)
moLecular interactions, thereforer may be both dipolar
and quadrupolar. It is interesting to note that one
can relate the mechanism of phase transitions to the
moLecular interactions from thermodynamical analyses
and considerations, aLthough there are some uncertainties
in est,irnation of the "normal" heat capacity.
0●
`
[283]
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[285]
‐
‐